Oznaka poročila: ARRS-RPROJ-ZP-2015/227 ZAKLJUČNO POROČILO RAZISKOVALNEGA PROJEKTA A. PODATKI O RAZISKOVALNEM PROJEKTU 1.Osnovni podatki o raziskovalnem projektu Ш13Ш Šifra projekta N1-0011 Naslov projekta GReGAS - Geometrijske reprezentacije in simetrije grafov, preslikav in drugih diskretnih struktur ter aplikacij v znanosti Vodja projekta 1941 Tomaž Pisanski Tip projekta N Projekti ESF in ERC Obseg raziskovalnih ur 18137 Cenovni razred B Trajanje projekta 07.2011 - 06.2014 Nosilna raziskovalna organizacija 1669 Univerza na Primorskem, Inštitut Andrej Marušič Raziskovalne organizacije -soizvajalke 588 Univerza v Ljubljani, Pedagoška fakulteta 1554 Univerza v Ljubljani, Fakulteta za matematiko in fiziko 2547 Univerza v Mariboru, Fakulteta za naravoslovje in matematiko 2975 ABELIUM d.o.o., raziskave in razvoj Raziskovalno področje po šifrantu ARRS 1 NARAVOSLOVJE 1.01 Matematika Družbenoekonomski cilj Naravoslovne vede - RiR financiran iz drugih virov (ne iz SUF) Raziskovalno področje po šifrantu FOS 1 Naravoslovne vede 1.01 Matematika B. REZULTATI IN DOSEŽKI RAZISKOVALNEGA PROJEKTA 2.Povzetek raziskovalnega projekta1 SLO Geometrične in druge reprezentacije grafov in kombinatoričnih struktur, ki temeljio na grafih imajo pomembne aplikacije v matematiki, računalništvu, socialnih omrežjih, kemiji, bioinformatiki, itd. Ob črpanju motivacije iz aplikacij je bil glavni cilj projekta, da skupaj s partnerji v EU razvijemo koherentno teorijo reprezentacij grafov s poudarkom na simetričnih in skoraj simetričnih strukturah oz. produktih. Projekt sestavlja pet tem. Tema 1: Reprezentacije in struktura grafov in drugih diskretnih struktur. Preučevali smo splošne vidike reprezentacij grafov z uporabo strukturnih lastnosti in informacije o simetriji in s tem prispevali k izgradnji teorije reprezentacij (enotski grafi, reprezentacije, krovi, itd.) Tema 2: Skoraj simetrične strukture in produkti. Študirali smo izbrane teme povezane z grafovskimi produkti posebnih družin grafov (grafi Sierpinskega, Fibonaccijeve kocke) s poudarkom na izbranih grafovskih invariantah, še posebej v povezavi s Wienerjevim indeksem. Tema 3: Reprezentacije simetričnih grafov. Z nadaljevanjem razvoja teorije točkovno-tranzitivnih grafov smo prispevali k boljšemu razumevanju, še posebej v povezavi z določenimi strukturnimi lastnosti grup avtomorfizmov grafov v kontekstu grafovskih reprezentacij simetričnih kombinatoričnih struktur. Posebno pozornost smo posvetili opisu kubičnih in 4-valentnih grafov, na katerih delujejo grupe ločno tranzitivno, ter klasifikaciji posebnih struktur iz katerih izvirajo zanimive (delne) geometrije (asociacijske sheme, krepko regularni grafi, kletke). Tema 4: Reprezentacije konfiguracij, zemljevidov in politopov. Raziskave so bile osredotočene na strukturne lastnosti, klasifikacijo in oštevilčenje konfiguracij, zemljevidov in politopov v povezavi z njihovimi kombinatoričnimi in geometričnimi reprezentacijami. Prav tako smo se osredotočali na razvoj usteznih algoritmov. Preučevali smo reprezentacije konfiguracij preko grafov in obratno, konstrukcije. Prav tako smo se osredotočili na klasifikacije novih razredov simetričnih konfiguracij z visoko stopnjo povezanosti. Tema 5: Reprezentacije velikih omrežij in aplikacije v kemiji, bioinformatiki in socialnih omrežjih. Velika omrežja z večimi milioni vozlišč so običajno redka in pri njihovi obravnavi se soočamo z določenimi tehnološkimi omejitvami (v celoti morajo biti shranjena v spominu). V projektu smo se osredotočili na omrežja citiranj, dvodelna omrežja in dinamična omrežja (analiza in vizualizacija). Identificirali in predstavili smo več možnosti aplikacij teorije grafov in zemljevidov v kemiji in sintetični biologiji. Rezultati projekta so objavljeni v več kot 40 člankih v znanstvenih revijah z impact faktorjem. Poročilo predstavlja le del projekta GReGAS v okviru sheme EUROCORES/EUROGIGA s strani Evropske znanstvene fundacije, ki smo ga izvajali v Sloveniji. ANG Geometric and other representations of graphs and graph based combinatorial structures have important applications in mathematics, computer science, social networks, chemistry, bioinformatics, etc. Motivated by applications, the main goal of the project was to, together with EU partners, develop a coherent theory of graph representations with emphasis on symmetric and near symmetric structures or products. The project consists of 5 themes. Theme 1: Representations and structure of graphs and other discrete structures. General aspects of graph representations using graph structural properties and information on symmetries have been studied, thus making the contribution towards building coherent representation theory (unit distance graphs, representation, covers, etc.) Theme 2: Near symmetric structures or products. Special topics related to graph products and special families of graphs were studied (Sierpinski graphs, Fibonacci cubes) together with particular graph invariants, especially Wiener index. Theme 3: Representations of symmetric graphs. By further developing theory of vertex-transitive graphs we have contributed to better understanding, especially of certain structural properties of automorphism groups of graphs in the context of graph representations of highly symmetric combinatorial structures. Special attention was given to description of cubic and quartic graphs admitting arc-transitive group actions and classification of special structures from which interesting (partial) geometries arise (association schemes, strongly regular graphs, cages). Theme 4: Representations of configurations, maps and polytopes. The research focused on structural properties, classification and enumeration of configurations, maps and polytopes relevant for their combinatorial and geometric representations, as well as on development of relevant algorithms. Relations between geometry and symmetries were studied in various geometries, both for finite and infinite structures. We have investigated representing configurations via graphs and vice versa, and studied construction and classification of new classes of symmetric highly incident configurations. Theme 5: Representations of large networks and applications in chemistry, bioinformatics and social networks. Large networks have several millions of vertices, are usually sparse and their use imposes certain technological limits (a need to store them completely in the computer memory). In the project, special attention was given to citation networks, two-mode networks and dynamic networks (analysis and visualization). Several applications of map and graph theory have been introduced to chemical graph theory and synthetic biology. The results of the project were published in more than 40 publications in journals with impact factor. The report presents only the part of the EUROCORES/EUROGIGA project GReGAS selected by European Science Foundation, which was carried out in Slovenia. 3.Poročilo o realizaciji predloženega programa dela na raziskovalnem projektu2 Projekt se je začel z julijem 2011 s t.i. "kick-off" sestankom v Parizu, kjer so se zbrali vodje vseh 4 projektov v programu EUROGIGA/EUROCORES in je bil določen program za aktivnosti mreženja. Slovenski del projekta je tako v okviru projekta organiziral naslednje mrežne aktivnosti: - simpozij CSASC 2011 v Kremsu, Avstrija, 2011 - SODO 2012 v Novi Zelandiji, - konferenco Computers in Scientific Discovery 6, 2013, Koper, Slovenija, - simpozij CSASC 2013 v Kopru, Slovenija, - GEMS 2013 na Slovaškem, Poleg tega pa se iz teh sredstev organizira tudi ravno tekoča konferenca EuroCD 2015 v Ljubljani, Slovenia (marec 2015). Projekt je naslavljal pet tem, ki so navedene v nadaljevanju z opisom rezultatov. 1. Reprezentacije in strukture grafov in drugih diskretnih struktur Preučevali smo grafe z enotsko razdaljo, t.j. take, ki jih lahko predstavimo v ravnini tako, da imajo vse povezave enako dolžino [COBISS.SI-ID 16312665]. Za pomembno družino grafov, to so posplošeni Petersenovi grafi, smo pokazali, da so grafi z enotsko razdaljo [COBISS.SI-ID 16217945]. Problema smo se lotili tako, da smo posplošene Petersenove grafe gledali v širšem kontekstu I-grafov in pokazali, da je vsak pospološeni Petersenov graf (razen nekaterih sporadičnih primerov, ki smo jih obravnavali posebej) izomorfen I-grafu, ki ima predstavitev z enotsko razdaljo v ravnini z rotacijsko simetrijo. Pri tem smo potrebovali tudi karakterizacijo za izomorfnost I-grafov z različnimi parametri [COBISS.SI-ID 16069977]. Na grafih z enotsko razdaljo smo preučevali tudi invariante, kot so dilacijski koeficient, ravninska širina ter resolucijski koeficient in odnose med njimi [COBISS.SI-ID 1024499540]. Vpeljali smo naravno posplošitev Petersenovih grafov, t.i. GI-grafe in popolnoma karakterizirali grupe avtomorfizmov za te grafe. To nam je omogočilo študij ostalih simetrijskih lastnosti, kot je točkovna tranzitivnost in kateri GI-grafi so Cayleyevi [COBISS.SI-ID 1024411732]. Definirali smo tudi posebne vrste krov nad poljubnim enostavnim grafom G in ga imenovali TheCov(G), ki je popolnoma določen z grafom. Študirali smo simetrijske in grafovske lastnosti takih krovov [COBISS.SI-ID 16868185]. Vzpostavili smo tudi Enciklopedijo grafov (http://atlas.gregas.eu), ki jo prav tako dalje podporamo v okviru infrastrukturnega programa na podjetju Abelium. Katalog 4-valentnih simetričnih grafov smo uspeli zapisati v zelo skrčeni obliki s pomočjo krovov. 2. Skoraj simetrične strukture in produkti grafov Na področju splošne teorije izometričnih vložitev smo eksplicitno določili kanonično izometrično vložitev za grafe Sierpinskega [COBISS.SI-ID 16582233]. Poleg tega smo za to dvoparametrično družino grafov določili oz. podali meje za Hammingovo dimenzijo [COBISS.SI-ID 16416857]. Nadalje smo karakterizirali grafe Sierpinskega, ki so vpeti podgrafi grafov Hanojskega stolpa [COBISS.SI-ID 16590425]. Preučevane so bile metrične invariante grafov, kar vključuje tudi polinomske funkcije, Wienerjev indeks na uteženih grafih in metrično dimenzijo grafa. Pokazali smo, da se lahko Wienerjev indeks uteženih grafov izrazi kot vsota Wienerjevih indeksev uteženih kvocientnih grafov glede na poljubno kombinacijo Djokovic-Winkler razredov. Dodatno smo pokazali da se lahko uporabi metoda rezov za izračun poljubnih momentov razdalj za vse grafe, ki so izometrično vložljivi v kartezični produkt trikotnikov [COBISS.SI-ID 16590169, 16861017, 16768089, 16861017, 16893273]. Študirali smo tudi konveksnost, še posebej pa lastnosti konveksnih ciklov. Podali smo zgornjo mejo za število konveksnih ciklov v danem grafu in pogazali da velja enakost če in samo če je graf lih cikel ali Moorov graf (en članek poslan v objavo). Preučevali so izometrične podgrafe hiperkock (ki so najenostavnejši večkratni kartezični produkti), predvsem Fibonaccijeve kocke in Lucasove kocke. Osredotočili smo se na različne metrike in povezane probleme na produktnih grafih, med katerimi so (i) k-potno vektorsko pokritje, ki je grafovska invarianta povezana z varnostnimi vidiki v brezžičnih omrežjih, (ii) b-barvanja v krepkih produktih, leksikografskih produktih in direktnih produktih, (iii) varnostno število na mrežnih grafih (mreže, cilinder, torus), (iv) particijska dimenzija krepkih produktov in Kartezičnih produtkov, (v) L(2,1)-označevanja produktov in L(3,2,1)-označevanja trikotniških in toroidalnih mrež, (vi) kromatično število in moč največje neodvisne množice kvadrata kartezičnih produktov ciklov. Na to temo je bilo objavljnih več del: [COBISS.SI-ID 16624473, 16590425, 16590169, 19464968, 17220697, 17087065,16970585]. Razen tega smo napisali pregledni članek (ki med vsebuje tudi nove krajše dokaze znanih izrekov) o Fibonaccijevih kockah in sorodnih razredih grafov in s tem dodatno osvetlili Fibonaccijevo dimenzijo grafa [COBISS.SI-ID 16603737] 3. Reprezentacije simetričnih grafov Na področju simetrij smo se ukvarjali z raziskavami snarkov in hamiltonskosti preko metode vlaganja grafov na ploskve. Raziskovalci na tem področju so dosegli izjemen uspeh s prestižno objavo [COBISS.SI-ID 1024390740]. Ukvarjali smo se s študijem krovnih grafov ter tudi z povezanostjo razdaljno uravnoteženih grafov [COBISS.SI-ID 1024329300]. Izvedli smo klasifikacijo visoko simetričnih grafov, med njimi kubičnih simetričnih tricirkulantov in tetracirkulantov, bicikličnih grafov z ektremnim PI-indeksom. Ukvarjali smo se tudi z študijem grup avtomorfizmov racionalnih cirkulantnih grafov. Na področju študija simetrij v grafih smo dalje študirali točkovno tranzitivne grafe. Točkovno tranzitivni grafi v splošnem kot tudi povezave med njimi in geometrijskimi objekti predstavljajo pomembno temo aktivnih raziskav že dlje časa. Večina interesa izvira iz dejstva da so primerni za modeliranje znanstvenih fenomenov povezanih s simetrijo. Naš cilj je bil raziskovati odprte probleme povezane s stukturnimi lastnostnmi točkovno tranzitivnih grafov, še posebej tistih, ki zadoščajo dodatnim grupno-teoretičnim lastnostim, kot so npr. ločna-tranzitivnost, pol-ločna-tranzitivnost in semisimetrična delovanja grup, s poudarkom na navezavo na odprte probleme na konfiguracijah in simetričnih zemljevidih. Dodatno smo uporabljali geometrijska orodja za reševanje problemov v teoriji točkovno tranzitivnih grafov, kot je zneni odprti problem Hamiltonovih poti/ciklov v točkovno tranzitivnih grafih. Na temo simetričnih grafov je bilo objavljenih več del COBISS.SI-ID: 1024446036, 1024510804, 1024533588, 1536117444,1536086724,1024490836,1024470868, 1024486996, 1024490324, 1536085700, 1024511060, 1024532564, 1024516948, 1536241092, 1536423620, 1536423620, 1536920004, 1536280516, 1537120964, 1536172996, 1536382660]. 4. Reprezentacije konfiguracije, zemljevidov in politopov Ukvarjali smo se s preučevanjem simetrijskih tipov zemljevidov na ploskvah ter vplivom operacij (duala) na njih [COBISS.SI-ID 16773465]. Objavili smo članek s klasifikacijo toroidalnih politopov, ki jih dobimo z razrezom prostorskega tlakovanja s kockami {4,3,4} [COBISS.SI-ID 16478297]. Vodja projekta prof. dr. Pisanski je v soavtorstvu z B. Servatius objavil tudi monografijo Configurations from a Graphical Viewpoint (Birkhäuser Advanced Texts Basler Lehrbücher) [COBISS.SI-ID 16418137]. Na področju učinkovitega generiranja grafov smo sodelovali z Univerzo v Gentu, Belgija [COBISS.SI-ID 16653401]. Objavljen je bil članek v povezavi s Haarovimi grafi in konfiguracijami [COBISS.SI-ID 1536194756]. Preučevali smo rotacijsko simetrične poligone in konfiguracije [COBISS.SI-ID 1024339284] Na področju študija geometrijskih reprezentacij konfiguracij smo študirali g-laterale in geometrične in kombinatorične konfiguracije. Pokazali smo, da se v posebni družini konfiguracij lahko pojavi ali pa ne katera koli od osmih možnih kombinacij obstoja ali neobstoja g-lateral za 3 < g < 5. Poleg tega smo prikazali geometrične realizacije za izbrane manjše primere 3-, 4- in 5-lateral prostih (v3) konfiguracij (posplošeni šestkotniki). Študirali smo tudi (v4) konfiguracije in identificirali najmanjšo znano geometrično 3-lateral prosto (v4) konfiguracijo. [COBISS.SI-ID 16089433] 5. Reprezentacije velikih omrežij in aplikacije v kemiji, bioinformatiki ter socialnih omrežjih. Razvili smo nove funkcionalnosti pri orodju net.Plexor, ki je alternativa orodju Pajek in se ga bo uporabljalo za analizo in vizualizacijo omrežij in ga ponudili v uporabo tudi v okviru infrastrukturnega programa na podjetju Abelium. V okviru izdelave programa se je izobraževalo več mladih raziskovalcev, ki so medtem že tudi doktorirali. Začel se je tudi razvoj na prototipnih programskih knjižnicah v Pythonu za časovna omrežja (TQ, Ianus). Objavljen je bil članek, ki omogoča vizualizacijo s pomočjo (X,Y)-gručenja [COBISS.SI-ID 16097881]. Izvajali smo raziskave na področju implementacije gručenja po povezavah in ustrezne vizualizacije, pri čemer je sodeloval še en študent (Jernej Bodlaj). V. Batagelj je skupaj z mlado raziskovalko v gospodarstvu Moniko Cerinšek objavil članek v reviji Scientometrics. Temeljila je na raziskavah na podatkovni bazi ZENTRALL BLATT for mathematics in sodelovalnih omrežjih avtorjev. Uvedene so bile ustrezne uteži v izračun omrežij sodelovanj, ki so omogočile realnejšo sliko prispevka (produktivnosti) posameznega avtorja in ustreznejše določitve skupin sodelujočih avtorjev. Poleg tega smo lahko vpeljali ustrezno mero za sodelovalnost posameznega avtorja [COBISS.SI-ID 17149273, 16739929]. Monografija W. de Nooy, A. Mrvar, V. Batagelj, Exploratory Social Network Analysis with Pajek: Revised and Expanded 2nd Edition., Cambridge University Press, Cambridge, GB, 2012 [COBISS.SI-ID 30443869], je doživela ponovno razširjeno izdajo, poleg tega pa je bila izdana tudi v kitajskem jeziku [COBISS.SI-ID 31870813]. Začeli in intenzivno delali smo na raziskavah na področju dinamičnih velikih omrežij. Rezultat dela je objavljena monografija [COBISS.SI-ID 31563993]. Prispevali smo več prispevkov v obsežno Encyclopedia of Social Networks Analysis and Mining [COBISS.SI-ID 17138265, 17138521,17138777,17145433]. Sodelovali smo pri analizi podatkov o telefonskem prometu v Slonokoščeni obali d4d (data for development). Rezultate smo predstavili na srečanju skupin na MIT, ZDA. Ukvarjali smo se z razvojem novih metod za analizo velikih acikličnih omrežij (npr. omrežja sklicevanj - citation networks). Razvili smo nov, zelo hiter postopek za določanje pomembnosti vozlišč - verjetnostni (pre)tok (probabilistic flow). Za uteži povezav SPC smo pokazali, da je utež na posamezni povezavi manjša ali enaka od uteži na povezavah na poti, ki veže njeni krajišči. Torej lahko tranzitivnostne povezave odstranimo in dobimo preglednejšo sliko omrežja - tranzitivnostno ogrodje (skelet). Razvili smo učinkovit postopek za določanje slednjega v velikih omrežjih. Na področju kemijske teorije grafov smo preučevali uporabo prapornih grafov na benzenoidih [COBISS.SI-ID 16058713], [COBISS.SI-ID 16971097]. Objavili smo tudi članek na temo zanimive povezave Jahn-Telleijevega izreka s teorijo grafov [COBISS.SI-ID 16090457], v prestižni reviji Proc. - Royal Soc., Math. phys. eng. sci. V povezavi z Jahn-Telleijevimi problemi pa je prišlo do objave še enega članka [COBISS.SI-ID 16411737]. Ukvarjali smo se z grafičnimi predstavitvami DNK v ravnini s pomočjo zemljevidov ter s kvantitativno in računsko analizo teh. Štiri-črkovna zaporedja smo predstavili s pomočjo spiralne reprezentacije nad trikotniško in štirikotniško mrežo v ravnini v obliki 4-obarvanega zemljevida. Preučevali smo razne matrične invariante. [COBISS.SI-ID 16842585] Študirali smo oblike reprezentacij spletnih strani in portalov s pomočjo grafov in predlagali različne organizacijske pristope. [COBISS.SI-ID 51728482]. 4.Ocena stopnje realizacije programa dela na raziskovalnem projektu in zastavljenih raziskovalnih ciljev3 Projekt se je izvedel v skladu z zastavljenimi cilji. Mednarodno sodelovanje je bilo uspešno. Angažirani smo tudi v mrežne aktivnosti v sodelovanju z ESF. V okviru tega poročila opisujemo samo del projekta, ki se je izvajal v Sloveniji in je bil financiran s strani ARRS. Projekt ima tudi mednarodno dimenzijo, ki pa je prikazana v poročilih za Evropsko znanstveno fundacijo. Oddani sta bili tudi vmesno in končno poročilo Evropski znanstveni fundaciji. Vmesno poročilo je bilo pozitivno ocenjeno končno pa je še v postopku ocenjevanja. Oddani poročili sta pripeti temu poročilu. 5.Utemeljitev morebitnih sprememb programa raziskovalnega projekta oziroma sprememb, povečanja ali zmanjšanja sestave projektne skupine4 V projektu ni večjih sprememb, kljub temu, da je s strani ARRS v letu 2012 in 2013 prišlo do znižanja sredstev. 6.Najpomembnejši znanstveni rezultati projektne skupine5 Znanstveni dosežek 1. COBISS ID 16739929 Vir: COBISS.SI Naslov SLO O bibliografskih omrežjih ANG On bibliographic networks Opis SLO V članku pakažemo, da lahko bibliografske podatke pretvorimo v nabor usklajenih omrežij. Z množenjem omrežij lahko iz njih pridobimo več zanimivih izpeljanih omrežij. Pri njihovi definiciji je potrebno upoštevati ustrezno normalizacijo. Predstavljeni pristop je uporaben tudi za podobne nabore usklajenih omrežij z drugih področij. Omrežja, pridobljena iz bibliografskih podatkovij, so lahko (zelo) velika (na sto tisoče vozlišč). K sreči so redka in jih za to še vedno lahko obdelamo razmeroma hitro. V članku damo odgovor na vprašanje: kdaj je zmnožek dveh redkih omrežij tudi sam redko omrežje. Predlagani pristopi so prikazani z analizo nabora omrežij na temo "social networks", pridobljenih iz Web of Science. Dela z velikim številom avtorjev dodajo običajnemu omrežju sodelovanj velike polne podgrafe in tako zameglijo sliko o sodelovanjih. Pokažemo, da lahko z ustrezno normalizacijo njihov učinek pridušimo. Med drugim vpeljemo mero sodelovalnosti avtorjev glede na dano bibliografijo in pokažemo, kako lahko izračunamo omrežje sklicevanj med avtorji in razkrijemo skupine glede na sklicevanje. ANG In the paper we show that the bibliographic data can be transformed into a collection of compatible networks. Using network multiplication different interesting derived networks can be obtained. In defining them an appropriate normalization should be considered. The proposed approach can be applied also to other collections of compatible networks. The networks obtained from the bibliographic data bases can be large (hundreds of thousands of vertices). Fortunately they are sparse and can be still processed relatively fast. We answer the question when the multiplication of sparse networks preserves sparseness. The proposed approaches are illustrated with analyses of collection of networks on the topic "social network" obtained from the Web of Science. The works with large number of co-authors add large complete subgraphs to standard collaboration network thus bluring the collaboration structure. We show that using an appropriate normalization their effect can be neutralized. Among other, we propose a measure of collaborativness of authors with respect to a given bibliography and show how to compute the network of citations between authors and identify citation communities. Objavljeno v Springer;Akademiai Kiado; Scientometrics; 2013; Vol. 96, iss. 3; str. 845864; Impact Factor: 2.274;Srednja vrednost revije / Medium Category Impact Factor: 1.031; A'': 1;A': 1; WoS: EV, NU; Avtorji / Authors: Batagelj Vladimir, Cerinšek Monika Tipologija 1.01 Izvirni znanstveni članek 2. COBISS ID 16090457 Vir: COBISS.SI Naslov SLO Teorija grafov in Jahn-Tellerjev izrek ANG Graph theory and the Jahn-Teller theorem Opis SLO Jahn-Tellerjev izrek napoveduje spontano razbijanje simetrije in dvig degeneriranih elektronskih stanj nelinearnih molekularnih sistemov. V takih primerih se to zgodi zaradi geometrijskega popačenja. Molekularni problemi so pogosto modelirani s spektralno teorijo za obtežene grafe. Pričujoči prispevek obrne proces v nasprotno smer in na novo formulira Jahn-Tellerjev izrek za splošne utežene grafe. Če razumemo lastne vektorje kot orbitale, lastne vrednosti pa kot energijske nivoje, ki naj bi jih zasedli elektroni, tedaj je mogoče degeneracijo stanj razrešiti z ne popolnoma simetrično porazdelitvijo uteži na povezavah in, če je potrebno tudi na vozliščih grafa. V tej zvezi je postavljena tudi zanimiva domneva. Posebej sta obravnavana dva primera (graf oktaedra in graf fenalenila) saj se pri njiju degeniranost pojavlja zaradi različnih razlogov. The Jahn-Teller (JT) theorem predicts spontaneous symmetry breaking and lifting of degeneracy in degenerate electronic states of (nonlinear) molecular and solid-state systems. In these cases, degeneracy is lifted by ANG geometric distortion. Molecular problems are often modelled using spectral theory for weighted graphs, and the present paper turns this process around and reformulates the JT theorem for general vertex- and edge-weighted graphs themselves. If the eigenvectors and eigenvalues of a general graph are considered as orbitals and energy levels (respectively) to be occupied by electrons, then degeneracy of states can be resolved by a non-totally symmetric re-weighting of edges and, where necessary, vertices. This leads to the conjecture that whenever the spectrum of a graph contains a set of bonding or anti-bonding degenerate eigenvalues, the roots of the Hamiltonian matrix over this set will show a linear dependence on edge distortions, which has the effect of lifting the degeneracy. When the degenerate level is non-bonding, distortions of vertex weights have to be included to obtain a full resolution of the eigenspace of the degeneracy. Explicit treatments are given for examples of the octahedral graph, where the degeneracy to be lifted is forced by symmetry, and the phenalenyl graph, where the degeneracy is accidental in terms of the automorphism group. Objavljeno v Royal Society; Proceedings. Series A, Mathematical, Physical and Engineering Sciences; 2012; Vol. 468, no. 2140; str. 971-989; Impact Factor: 2.378;Srednja vrednost revije / Medium Category Impact Factor: 2.514; A': 1; WoS: RO; Avtorji / Authors: Ceulemans Arnout, Lijnen E., Fowler Patrick W., Mallion Roger B., Pisanski Tomaž Tipologija 1.01 Izvirni znanstveni članek 3. COBISS ID 1024390740 Vir: COBISS.SI Naslov SLO 1024390740 ANG Hamilton cycles in (2, odd, 3)-Cayley graphs Opis SLO Leta 1969 je Lovasz postavil vprašanje, ali ima vsak končen, povezan točkovno-tranzitiven graf Hamiltonovo pot. Kljub enostavni formulaciji, do sedaj ni bil dosežen kak večji preboj in sedaj je splošno sprejeto, da gre za težek problem. Enako velja za poseben podrazred Cayleyevih grafov, kjer je postavljena domneva o obstoju Hamiltonovih ciklov. Leta 2007 sta Glover in Marušič dokazala, da ima Cayleyev kubični graf za končno $ (2, i, 3) $-generirano grupo $G = \ langle, x | л 2 = x л y = (ax) л 3 = 1, \ dots \ rangle $ ? Hamiltonsko pot, če je $ | G | $ kongruentna 0 po modulu 4, in ima Hamiltonski cikel, če je $ |G| $ kongurentna 2 po modulu 4. Konstruiran je bil Hamiltonov ciklel na osnovi kombinacije teorije Cayleyevih zemljevidov s klasičnimi rezultati o ciklični stabilnosti v kubičnih grafih, in sicer kot v točko stisljiv rob drevesa lic pripadajočega Cayleyevega zemljevida. Z posplošitvijo teh motod so Glover, Kutnar in Marušič v letu 2009 razrešili še primer, ko je poleg $ | G | $ še $s$ kongruenten 0 po modulu 4. V tem članku je z dodatno razširitvijo pristopa z "drevesom lic" dokazano, da ostaja Hamiltonov cikel tudi ko je $ | G | $ kongruentna 0 po modulu 4 in je $s$ lih. S tem ostane kot edini odprt primer še, ko je $ | G | $ kongruentna 0 po modulu 4 in je $s$ kongruentno 2 po modulu 4. V tem zadnjem primeru pristop preko "drevesa lic" ni mogoče uporabiti in tako bo za dokončanje dokaza o obstoju Hamiltonovih ciklov v kubičnih Cayleyevih grafih, ki izhajajo iz končnih ? $ (2, i, 3) $-generiranih grup, potrebno uporabiti popolnoma nove in drugačne metode. In 1969, Lovasz asked if every finite, connected vertex-transitive graph has a Hamilton path. In spite of its easy formulation, no major breakthrough has been achieved thus far, and the problem is now commonly accepted to be very hard. The same holds for the special subclass of Cayley graphs where the existence of Hamilton cycles has been conjectured. In 2007, Glover and Marušič proved that a cubic Cayley graph on a finite $(2, s, 3)$-generated group $G = \langle a, x| a^2 = x^s = (ax^3 = 1, \dots ANG \rangle$ has a Hamilton path when $|G|$ is congruent to 0 modulo 4, and has a Hamilton cycle when $|G|$ is congruent to 2 modulo 4. The Hamilton cycle was constructed, combining the theory of Cayley maps with classical results on cyclic stability in cubic graphs, as the contractible boundary of a tree of faces in the corresponding Cayley map. With a generalization of these methods, Glover, Kutnar and Marušič in 2009 resolved the case when, apart from $|G|$, also $s$ is congruent to 0 modulo 4. In this article, with a further extension of the above "tree of faces" approach, a Hamilton cycle is shown to exist whenever $|G|$ is congruent to 0 modulo 4 and s is odd. This leaves $|G|$ congruent to 0 modulo 4 with s congruent to 2 modulo 4 as the only remaining open case. In this last case, however, the "tree of faces" approach cannot be applied, and so entirely different techniques will have to be introduced if one is to complete the proof of the existence of Hamilton cycles in cubic Cayley graphs arising from finite $(2, s, 3)$-generated groups. Objavljeno v Clarendon Press; Proceedings of the London Mathematical Society; 2012; Vol. 104, no. 6; str. 1171-1197; Impact Factor: 1.151;Srednja vrednost revije / Medium Category Impact Factor: 0.673; A': 1; WoS: PQ; Avtorji / Authors: Glover Henry, Kutnar Klavdija, Malnič Aleksander, Marušič Dragan Tipologija 1.01 Izvirni znanstveni članek 4. COBISS ID 16582233 Vir: COBISS.SI Naslov SLO O razdaljah v grafih Sierpinskega: skoraj-ekstremna vozlišča in metrična dimenzija. ANG On distances in Sierpinski graphs: almost-extreme vertices and metric dimension Opis SLO Grafi Sierpinskega $S_p^$ tvorijo intenzivno raziskovano družino grafov fraktalne narave. Uporabni so v topologiji, matematiki Hanojskega stolpa, računalništvu, ter drugod. V članku vpeljemo skoraj-ekstremna vozlišča grafa $S_p^$ kot vozlišča, ki so bodisi sosedna z nekim ekstremnim vozliščem, ali pa so incidenčna povezavi med dvema podgrafoma izomorfnima $S_p^n-1}$. Podane so eksplicitne formule za razdalje v $S_p^n}$ med poljubnim vozliščem in skoraj-ekstremnim vozliščem. Formule so uporabljene za izračun celotne razdalje skoraj-ekstremnih vozlišč in za določitev metrične dimenzije grafov Sierpinskega. ANG Sierpinski graphs $S_p^$ form an extensively studied family of graphs of fractal nature applicable in topology, mathematics of the Tower of Hanoi, computer science, and elsewhere. An almost-extreme vertex of $S_p^$ is introduced as a vertex that is either adjacent to an extreme vertex of $S_p^$ or is incident to an edge between two subgraphs of $S_p^n}$ isomorphic to $S_p^n-1}$. Explicit formulas are given for the distance in $S_p^n}$ between an arbitrary vertex and an almost-extreme vertex. The formulas are applied to compute the total distance of almost-extreme vertices and to obtain the metric dimension of Sierpinski graphs. Objavljeno v Faculty of Electrical Engineering, Department of Applied Mathematics; Applicable analysis and discrete mathematics; 2013; Vol. 7, no. 1; str. 7282; Impact Factor: 0.708;Srednja vrednost revije / Medium Category Impact Factor: 0.674; WoS: PN, PQ; Avtorji / Authors: Klavžar Sandi, Zemljič Sara Sabrina Tipologija 1.01 Izvirni znanstveni članek 5. COBISS ID 1536241092 Vir: COBISS.SI Naslov SLO Pol-ločno-tranzitivni grafi z majhnim številm alter-mrež ANG Half-arc-transitive graphs with small number of alternets Grafu X rečemo da je G-pol-ločno tranzitiven, če G= 12 have polytopes of rank ?(n-1)/2?, SIAM Journal on Discrete Math. 26 (2012), nr. 2, 482-498; M.I.Hartley, I.Hubard, D. Leemans. Regular 4-polytopes from the Livingstone graph of Janko's first group, J. Alg. Combi. 35 (2012), 193-214. M.-E.Fernandes, D. Leemans, M. Mixer. Polytopes of high rank for the alternating groups. J. Combin. Theory Ser. A 119 (2012), 42-56; M.-E.Fernandes, D. Leemans. Polytopes of high rank for the symmetric groups, Adv. Math. 228 (2011), 32073222; Leydold, Josef. 2012. Dendrimers are the unique chemical trees with maximum spectral radius. MATCH Communications in Mathematical and in Computer Chemistry 68 (3): 851-854. News & Views-type articles / Other articles (please define) / - Books As editor(s) /_ As author(s) or author(s) of chapters R. Nedela, M. Škoviera: Maps. Section 7.6 (42 pp.) in Handbook of Graph Theory, eds. J. Yellen, J. Gross, 2nd ed, in press. Pisanski, Tomaž, Servatius, Brigitte, Configurations from a Graphical Viewpoint, Birkhäuser Advanced Texts Basler Lehrbücher, Birkhäuser Basel. 2013, XIII, 279 p. 274 illus., 45 in color. Klemm, Konstantin and Stadler, Peter F., Theory and Principled Methods for Designing Metaheustics, Elementary Landscapes (Borenstein, Yossi and Moraglio, Alberto eds.). Springer, Berlin, 2013 in press. Bresar, Bostjan and Kovse, Matjaz and, Geodetic sets in graphs.Structural analysis of complex networks , Birkhauser Springer, New York, 2011, 197--218. http://dx.doi.org/10.1007/978-0-8176-4789-6_8 Vukicevic Damir, "Applications of perfect matchings in chemistry", Book: " Structural analysis of complex networks", Birkhäuser/Springer, New York, 2011, Pages=463--482 Chapter: P.W. Fowler, A. Graovac: The Estrada Index and Fullerene Isomerism. Chapter 14, pp 265-280, In Mathematics and Topology of Fullerenes, Eds. F. Cataldo A. Graovac, O. Ori, , Carbon Materials: Chemistry and Physics 4 , Springer, New York, 2011. Cicalese, Ferdinando and Milani\vc, Martin and Vaccaro, Hardness, approximability, and exact algorithms for vector.Fundamentals of computation theory Lecture Notes in Comput. Sci. (6914), Springer, 2011, 288--297. http://dx.doi.org/10.1007/978-3-642-22953-4_25 Cicalese, Ferdinando and Milani\vc, Martin, Graphs of separability at most two: structural.Combinatorial algorithms Lecture Notes in Comput. Sci. (6460), Springer, 2011, 291--302. http://dx.doi.org/10.1007/978-3-642-19222-7_30 Kami\'nski, Marcin and Medvedev, Paul and Milani\vc, Shortest paths between shortest paths and independent sets.Combinatorial algorithms Lecture Notes in Comput. Sci. (6460), Springer, 2011, 56--67. http://dx.doi.org/10.1007/978-3-642-19222-7_7 Hammack, Richard and Imrich, Wilfried and Klav{\v{z}}ar, Sandi, Handbook of product graphs, Second Edition. Discrete Mathematics and its Applications (Boca Raton). CRC Press. 2011 - Other Please define (data products, video, etc.)_ • net.Plexor - will be collected from contributions (http://www.abelium.eu/development/net.plexor) • GReGAS Atlas - Encyclopedia of Graphs (http://atlas.gregas.eu/) • Batagelj. V., A. Mrvar, A. WoS2Pajek 1.0 (October 2011). A program for transforming WoS data into corresponding Pajek networks. Python source http://pajek.imfm.si/lib/exe/fetch.php?media=dl:wos2pajek10.zip • V. Batagelj. Preprint 0.3 (Jun 2012). A program for transforming citation networks with some small strong components into corresponding acyclic network. Python source: http://pajek.imfm.si/lib/exe/fetch.php?media=dl:preprint.py Presentations in scientific meetings - Oral presentations (indicate invited / keynote talks) 7th Slovenian International Conference on Graph Theory, Bled, Slovenia, June 2011 (majority of project members, invited speakers: Škoviera, Imrich, Schulte) T. Pisanski. Meeting "Mathematics and Art", Ljubljana, Slovenija, June 2011 T. Pisanski. Workshop on Symmetry in Graphs, Maps, and Polytopes, Toronto, Canada, October 2011 (invited speaker) T. Pisanski. The 35th Australasian Conference on Combinatorial Mathematics & Combinatorial Computing, Monash University, Melbourne, Australia, December 2011 Batagelj Vladimir, Cerinšek Monika, Horvat Boris: Network analysis of Zentralblatt MATH data. 7th Slovenian International Conference on Graph Theory, Jun 2011, Bled, Slovenia. Bodlaj Jernej, Batagelj Vladimir, Orbanić Alen: OpenGL® Graphical User Interface for net.Plexor - Interactive Large Network Analysis Library. 7th Slovenian International Conference on Graph Theory, Jun 2011, Bled, Slovenia. Batagelj Vladimir, Cerinšek Monika, Horvat Boris, Pisanski Tomaž: Exploring the structure of mathematical publications, CSASC 2011, September 2011, Krems, Austria. Batagelj Vladimir, Cerinšek Monika, Horvat Boris, Pisanski Tomaž: The structure of mathematics from Zentralblatt MATH data. 16th Young Statisticians Meeting, October 2011, Rijeka, Croatia. Batagelj Vladimir, Cerinšek Monika, Horvat Boris, Pisanski Tomaž: The structure of mathematics from the Zentralblatt MATH data base. Sunbelt XXXII, March 2012, Redondo Beach, CA, USA. Breznik Kristijan, Batagelj Vladimir: Network analysis of tennis games in the Open Era. Sunbelt XXXII, March 2012, Redondo Beach, CA, USA. Sandi Klavžar: Fibonacci cubes, generalized Fibonacci cubes, and bad words, invited plenary talk at Combinatorics 2012, Perugia, Italy, September 2012 (invited talk). Sandi Klavžar: Generalized Fibonacci cubes and three related problems on binary words, invited plenary talk at The 21st Workshop 3in1', Krakow, Poland, November 2012 (invited talk). Aleksander Vesel: Linear recognition and embedding of Fibonacci cubes, talk at Combinatorics 2012, Perugia, Italy, September 2012 (invited talk). Math Chem Comp, Dubrovnik (13.6.-18.6.2011) // Snjezana Majstorovic, Antoaneta Klobucar:K-domination on hexagonal chain cacti (talk) EuroGiga Midterm Conference, July 2012, Prague, Czech Republic // Snjezana Majstorovic: Domination on m-ary chain cacti (talk) 8th Meeting of the International Academy of Mathematical Chemistry, June 2012, Verona, Italy // Snjezana Majstorovic: Bounds and relations involving betweenness centrality in some families of graphs (talk) MATH/CHEM/COMP 2011 (Dubrovnik) // Sedlar Jelena, Vukičević Damir, Rajtmajer Sarah Michele, "On ordering alkanes by modified Zagreb indices" // 7th Slovenian International Conference on Graph Theory (Bled, 2011) //D. Vukičević, "Community detection in complex networks" Dragan Marušič, On two open problems in vertex-transitive graphs, "Beijing International Workshop on Group Actions on Combinatorial Structures'', August 21 - 27, 2011, Beijing, China. (INVITED TALK). Klavdija Kutnar, Classification of cubic symmetric polycirculants, "Beijing International Workshop on Group Actions on Combinatorial Structures'', August 21 - 27, 2011, Beijing, China. (INVITED TALK). Edward Dobson, Which Johnson graphs and folded Johnson graphs are Cayley graphs, "Beijing International Workshop on Group Actions on Combinatorial Structures'', August 21 - 27, 2011, Beijing, China. (INVITED TALK). Dragan Marušič, Searching for snarks amongst Cayley graphs, "CID 2011 Colourings, Independence and Domination 14th WORKSHOP ON GRAPH THEORY'' September 18 - 23, 2011, Szklarska Poreba, Poland. Klavdija Kutnar, Cubic Cayley graphs and snarks, "Workshop on Symmetry in Graphs, Maps, and Polytopes'', October 24-27, 2011, the Fields Institute, Toronto, Canada (INVITED TALK). Dragan Marušič, Half-arc-transitive graphs - possible research directions, "Workshop on Symmetry in Graphs, Maps, and Polytopes'', October 24-27, 2011, the Fields Institute, Toronto, Canada. Aleksander Malnič, On the Split Structure of Lifted Groups, "Workshop on Symmetry in Graphs, Maps, and Polytopes'', October 24-27, 2011, the Fields Institute, Toronto, Canada . Klavdija Kutnar, Quasi m-Cayley strongly regular graphs, "SODO2012 - Symmetries of Discrete Objects", February 13 - 17, 2012, Queenstown, New Zealand. Aleksander Malnič, On the split structure of lifted groups, I, "SODO2012 - Symmetries of Discrete Objects" February 13 - 17, 2012, Queenstown, New Zealand. Klavdija Kutnar, Cubic Cayley graphs and snarks, International Conference on Cycles in Graphs, Nashville, USA, May 30 - June 2, 2012 (Invited Speaker). Dragan Marušič, Hamiltonicity of cubic Cayley graphs, International Conference on Cycles in Graphs, Nashville, USA, May 30 - June 2, 2012 (Invited Speaker). Istvan Kovacs, Characterization of cyclic Schur groups, AAA84 84th Workshop on General Algebra, Dresden, Germany, June 8 - 10, 2012 Klavdija Kutnar, Distance-transitive graphs admit semiregular automorphisms, MDA 2012 - Mathematics of Distances and Applications, Varna, Bulgaria, July 2 - July 5, 2012 (Invited Speaker). Dragan Marušič, An infinite family of half-arc-transitive graphs with universal reachability relation, MDA 2012 -Mathematics of Distances and Applications, Varna, Bulgaria, July 2 - July 5, 2012 (Invited Speaker). Aleksander Malnič, On the split structure of lifted groups, I, MDA 2012 - Mathematics of Distances and Applications, Varna, Bulgaria, July 2 - July 5, 2012 (Invited Speaker). Martin Milanič, Equistable graphs: conjectures, results, and connections with Boolean functions, 25th European Conference on Operational Research, Vilnius (Lithuania), July 8-11, 2012. Martin Milanič, Uniqueness of independence polynomials in monogenic graph classes, International Colloquium on Graphs and Optimization 2012, Leukerbad, Switzerland, August 13-17, 2012. 7th Slovenian International Conference on Graph Theory 19-25 June 2011, Bled, Slovenia • Martin Skoviera: Snarks - Recent development (keynote lecture) • Jan Karabaš: Classification of Edge-transitive Maps Michal Kotrb'cfk: High-genus Embeddings • Martin Ma"caj: Nonorientable Regular Maps Over Linear Fractional Groups • Roman Nedela: Asymptotic Enumeration of ReversibleMaps Regardless of Genus 23rd British Combinatorial Conference University of Exeter, 4-8 July, 2011. • Jozef Siran, Nonorientable regular maps of any given type over linear fractional groups IWONT 2011 International Workshop on Optimal Network Topologies Brussels, Belgium, July 11 - 15, 2011 • Jana Siagiova: Cayley graphs in the degree-diameter problem (keynote lecture) • Martin Knor: On 3-arc graphs • Martin Macaj: Search for properties of the missing Moore graph • Maria Zdimalova: A family of large vertex-transitive graphs of diameter 2 Group Actions on Combinatorial Structures Beijing, August 21-27, 2011 • Martin Skoviera Regular maps with nilpotent automorphism groups • Jan Karabaš: Discrete groups of automorphisms of orientable surfaces • Roman Nedela: Discrete groups of automorphisms of surfaces with given genus • Jozef Siran: External symmetries of regular maps Workshop on Symmetry in Graphs, Maps, and Polytopes Fields Institute Toronto, October 24-27, 2011 • Martin Skoviera: Regular maps with nilpotent automorphism groups • Jan Karabas: Classification of edge-transitive maps • Martin Macaj: Nonorientable Regular Maps and Residual Finiteness of Triangle Groups • Roman Nedela: Vertex Transitive and Edge Transitive Polytopes and 2-Dimensional Orbifolds • Jozef Siran: External Symmetries of Regular and Orientably Regular Maps AMS Special Session on Topological Graph Theory, Structure and Symmetry, Boston, January 4-7, 2012 • Martin Skoviera: Locally Maximal Embeddings of Graphs in Orientable Surfaces (invited lecture) • Roman Nedela: A recent progress in map enumerations (invited lecture) • Roman Nedela: Vertex transitive polyhedral maps and actions of discrete groups on surfaces (invited lecture) ATCAGC 2012 Workshop on Algebraic, Topological and Complexity Aspects of Graph Covers 26th - 31st January 2012, Eugene, Oregon • Roman Nedela: Flows and graph coverings SODO 2012 Symmetries of Discrete Objects Conference and MAGMA Workshop Queenstown, New Zealand, 1217 February 2012 • Jan Karabas: Discrete group actions on orientable surfaces • Martin Macaj: On the Wilson operators • Jozef Siran: Imprimitivity of locally finite, 1-ended, planar graphs Eurogiga Midterm Conference Prague, July 9-13, 2012 • Martin Skoviera: Regular maps with nilpotent automorphism groups (invited lecture) IWONT 2012 The 5th International Workshop on Optimal Network Topologies July 27 - 29, 2012 Institut Teknologi Bandung, Indonesia • Jozef Siran: A survey of algebraic methods in the degree-diameter problem (keynote lecture) • Martin Knor: Graphs with given degree and diameter on the smallest number of vertices • Jana Siagiova: Quotients of large vertex-transitive and Cayley graphs of given degree and diameter ACCOTA 2012 International Workshop Combinatorial and Computational Aspects of Optimization, Topology and Algebra December 3 to 7, 2012. Huatulco, Oaxaca, Mexico • Martin Skoviera: Odd decompositions of regular eulerian graphs of odd orders • Jozef Siran: Algebraic methods in the degree-diameter problem Associate partners Berman, L. W. Fields Institute Thematic Program on Discrete Geometry and Applications: Workshop on Symmetry in Graphs, Maps and Polytopes, Oct 24 -- 27, 2011, http://www.fields.utoronto.ca/programs/scientific/11-12/discretegeom/talks/october.html M. Conder. The smallest regular polytopes of each rank'. Presented at 35th Australasian Conference on Combinatorial Mathematics and Combinatorial Computing, Melbourne, Australia, December 2011 M. Conder. A new approach to finding covers of arc-transitive graphs'. Presented at Workshop on Algebraic, Topological and Complexity Aspects of Graph Covers (ATCAGC 2012), Eugene, Oregon, USA, January 2012. M. Conder. Finitely-presented groups in MAGMA'. Presented at Conference on Symmetries of Discrete Objects (SODO 2012), Queenstown, New Zealand, February 2012. M. Conder. The orders of symmetric graphs'. Presented at SIAM Conference on Discrete Mathematics, Halifax, Nova Scotia, Canada, June 2012. M. Conder. The intersection condition for regular polytopes'. Presented at Workshop on Abstract Polytopes (WAP 2012),_ Cuernavaca, Mexico, July 2012. M. Conder. Graph Symmetries'. Presented at 36th Australasian Conference on Combinatorial Mathematics and Combinatorial Computing (36ACCMCC), Sydney, Australia, December 2012. P. W. Fowler. Ruđer Bošković Institute, Zagreb, 3 July 2012. Invited lecture in series: Eminentni znanstvenici na IRB (Distinguished Scientists at the RBI) Fries numbers of benzenoids - even faulty algorithms can be interesting (invited talk) P. W. Fowler. Croatian Academy of Sciences and Arts, Invited lecture 'Aromaticity and counting', November 2012. (invited talk) P. W. Fowler. Invited contributor to Fields Institute of Mathematics (Toronto) to meeting on mathematical asp Rigidity and Symmetry, Oct 2011 (invited talk) M. Klin. conference SSAOS 2012 (High Tatras) see https://sites.google.com/site/ssalgebra2012/program Title: New non-Schurian association schemes with a few clases (invited talk) W. Imrich. 13.-17. February, 2012. SODO 2012, Conference on "Symmetries of Discrete Objects". Queenstown, New Zealand Lecture "Distinguishing Infinite Graphs". W. Imrich. 12. March, 2012, Lecture in Maribor "Distinguishing Infinite Graphs". W. Imrich. 28.-31. March and 15.-19. April, 2012 (Blocked course, three weeks). AGH Cracow, "The direct product and large networks". W. Imrich. 4. May till 14. June, 2012 Graph Theory Semester, University of Primorska, Koper, Slovenia Lectures on "Symmetry Breaking in Graphs" W. Imrich. 24.-30. June, 1012. 3rd SYGN Workshop and 2012 PhD Summer School Discrete Mathematics Rogla, Slovenia W. Imrich. 1.-5. Juli 2012. 6th European Congress of Mathematics, Cracow. Lecture "The endomorphism distinguishing number of graphs". W. Imrich. 18. September, 2012. Lecture at Renyi Institute of the Academy of Sciences . in budapest on "Symmetry Breaking in Graphs". W. Imrich. 20. September, 2012. 10 Years Bioinformatics Leipzig W. Imrich. 1.-3. October 2012. International Symposium on Complex Network Analysis UMIT, Hall in Tirol Lecture on "Networks and Products of Graphs". W. Imrich. 19. October 2012. Lecture in Klagenfurt "Netzwerke". W. Imrich. 12. November 2012. Lecture University of Maribor "Symmetry Breaking in Graphs". W. Imrich. 25. November until 7. December, 2012 (Two-week blocked course) in Cracow on "Symmetry breaking in graphs". (More detailed than in Koper.) W. Imrich. 21st Workshop '3in1' 2012, Cracow, Poland. 29. November - 1. December 2012. Lecture "On the infinite Motion conjecture for Graphs and Groups". D. Leemans: Symmetries of Discrete Objects 2012, Queenstown (New Zealand), Febru- ary 13-17, 2012. Magma Minicourse on Permutation Groups, 2 lectures. D. Leemans: New Zealand Mathematical Society Colloquium, Auckland (New Zealand), December 6-8, 2011. Polytopes of high rank for the symmetric groups. D. Leemans: Workshop on Symmetry, Graphs and Polytopes, Fields Institute, Toronto (Canada), October 24-27, 2011. Plenary talk. Polytopes of high rank arising from almost simple groups. D. Leemans: Seventh Slovenian International Conference on Graph Theory, Bled (Slovenia), June 20-25, 2011. Chirally regular polytopes. D. Leemans: 5th De Bru n Workshop on Groups, Combinatorics and Computing, NUI Galway (Ireland), April 1116, 2011. Searching for Geometries with Magma. Leydold, Josef. 2011. Convex Cycle Bases and Cartesian Products. 25th LL-Seminar on Graph Theory, Leoben, Österreich, 23.09.-24.09. Leydold, Josef. 2012. Generating Generalized Inverse Gaussian Distributed Random Variates. Monte Carlo and Quasi-Monte Carlo Methods 2012, Sydney, Australien, 13.02.-17.02. Leydold, Josef. 2011. Convex Cycle Bases. 7th Slovenian International Conference on Graph Theory, Bled, Slowenien, 20.06.-24.06._ - Posters Computers in Scientific Discovery conference, August 2012, Portoroz (Slovenia) // Ivona Puljic: Upper and lower bound for Roman domination number of cardinal product of paths, (which was a joint work with Croatian PI Antoaneta Klobucar) - Other (please define) Balakrishnan, R. and Bapat, R. B. and Klav\vzar, Sandi and, Preface [Recent trends in graph theory and combinatorics].Discrete Math. 312 (2012), 1493. http://dx.doi.org/10.1016Zj.disc.2011.12.025 (Introduction) Bratislava Graph Theory Seminar (Regular seminar on graph theory and combinatorics) Head of the seminar: Martin Skoviera Weekly (during the semester) at Comenius University, Bratislava Slovakia Seminar for Discrete Matematics, Institute of Mathematics, Physics and Mechanics, Ljubljana. Head of the seminar: Tomaž Pisanski. Annual meeting of the slovak part of the GReGAS team. December 5 to 12 2011 and December 11 to 15 2012 Mosonmagyarovar, Hungary AGT in BB Algebraic Graph Theory in Banska Bystrica, August/September 2012, Matej Bel University, Banska Bystrica Slovakia • Programme Committee: Mikhail Klin, Roman Nedela and Martin Macaj (all members of GReGAS) • Organizing Committee: Martin Macaj, Jan Karabas (both GReGAS) and Stefan Gyurki In addition, Slovenian PL and PI teams achieved the following: • Organization of the conference Computers in Scientific Discovery with a plenary speaker, prof. Harold Kroto, nobel laureate (discovery of C60 fulleren) • proj. member prof. Konvalinka received award of University of Ljubljana given to best teachers. • A project financed by Picker Institute (USA, Colgate University) continued into the 2nd year as the results for the first year were very good. • Pisanski appointed to the Publications Committee of European Mathematical Society. • PI prof. Marusic was elected as rector of the University of Primorska. • project member prof. Miklavic received national award for science (Zois prize). Unpublished lecture: Leydold, Josef. 2012. Sign patterns of graph laplacian eigenvectors. Istanbul Discrete Mathematics Meetings, Istanbul, 27.04. Public outreach - Press releases (see below) - National / international newspaper articles (presenting your CRP or part of your work) Article related to the conference and EUROGIGA networking event and especially about nobelist Sir Harald Kroto visiting Slovenia having talk at CSD 6 conference. • http://www.dnevnik.si/magazin/znanost-in-tehnologija/1042548265 • http://www.primorska.info/novice/18840/nobelovec_kroto_predaval_na_turistici • http://www.slomedia.it/dr-kroto-znanost-je-predvsem-nacin-razmisljanja - TV appearance Croatian Academy of Sciences and Arts, Invited lecture 'Aromaticity and counting', November 2012. (invited talk) Short interview about this second lecture was recorded for Croatian TV - Radio appearance / - Other (please define) / Other activities / outputs - Patents / - Websites http://www.gregas.eu - Official project web site http://atlas.gregas.eu - Encyclopedia of graphs web site - Other (please define) • Abelium team: won Slovenian innovation award for the most innovative service iOliva (geometric graph theory application) B.5. Feedback on the EUROCORES programme and EUROCORES scheme Any other comments on the EUROCORES programme in particular or the EUROCORES scheme in general. 7 Priloga 2 GReGAS EuroGIGA Final report (Sections B and C) Deadline: 1/12/2014 Section B. Progress report Bl. CRP progress and scientific highlights (max. 1500 words) 1. The collaborative work (c.400-750 words) a. With reference to the CRP objectives and work plan, describe the work undertaken by the CRP and the contribution of each Individual Project to the collaboration in terms of its specific expertise and tasks/responsibilities. How closely did the partners work together? Pll-Pisanski o Encyclopaedia of Graphs was established. Several algorithms developed. o Theory of maps (type graphs) was extended, used on chemical graphs. Various classes of maps were classified. o Geometric representations for curves were studied. o Graph representations in chemical graph theory, quantum mechanics approaches with further applications were studied. PI2-Batagelj o Algorithms and visualization methods within the libraries net.Plexor, TQ and lanus were developed, o Extensive analysis of scientific collaboration database ZENTRALL BLATT for mathematics was carried out. o Dynamic networks were studied. PI3-Biyikoglu o Classification of graphs achieving minimum algebraic connectivity. o Study of power allocation and partner selection polices problems in wireless networks, molecular dendrimers, spectral radius, maximum Collatz-Sinogowitz index; relationships between graph invariants; spectral bounds for maximum induced matching problem o Analysis of metabolic pathways, work on de novo peptide sequencing o Modeling social communication (anonymity) with graph theory. PI4-Klavzar o Study of Hamming dimension of a graph, Sierpinski graphs; the structure of Fibonacci cubes o Sierpinski graphs were compared with Hanoi graphs w.r.t. their spanning embeddings o Metric invariants were investigated, including distance polynomial functions, Wiener index in weighted graphs, and metric dimension of graphs (papers submitted) o Convexity was investigated, especially the extremal properties of convex cycles, o Lambda-labelling of product graphs and related classes were studied. PI5-Klobucar o Large networks: Wiener index and edge decomposition, eccentric connectivity index, social networks o Graph representations in mathematical chemistry and bioinformatics:, pi-electron currents, conjugated circuits, forcing number, upper and lower bounds on bond incident degree indices. Bond additive modelling. Atom bond connectivity index. K-domination on Hexagonal Catus Chains o Roman-dominations on cardinal product of path and cycles studied. PI6-Marusic o Study ofHamilton paths/cycles in cubic: Cayley graphs arising from certain groups; graph covers; connectivity of distance balanced graphs, o Classification of highly symmetric graphs: cubic symmetric tricirculants and tetracirculants, bicyclic graphs with extremal values of Pl-index, automorphism groups of rational circulant graphs, o Applications in cryptography, geometric representations PI7-Škoviera o Graphs embeddings and immersions and highlysymmetric maps, work on classification of certain types of groups and related embeddings/maps into surfaces, 2-groups, complete bipartite graph embeddings, regular maps with nilpotent automorphism groups, embeddings of n-dimensional cube graphs, construction of self-dual and self-Petrie regular maps, asymptotic formulas for certain classes of maps, relation between genus and cycle space, local maxima in the stratified system of all graph embeddings described, o Colourings,flows and configurations. Sufficient condition in terms of point-line configurations for a Steiner triple system to be universal derived. The existence of 4-line Fano colourings for a very general class of snarks confirmed. Study of snarks, optimal acyclic edge-colourings of cubic graphs. (PI 8, Stadler) o Exploration of connection between the geometric graph models of molecules and polymers and the graphs that represent the relationships among them o Survey about hypergraph products has been published, o Characterization of retracts of Cartesian products of chordal graphs, o Characterization of recombination on strings as transit function was done, o A unified framework for linear and circular multiple sequence alignments was established, o A new formalization of graph editing, relaxed square property and topology of elementary cycles, connective spaces and application is landscape theory were studied. (AP 1, Conder/Leemans) o Work on regular covers (with PI6); Symmetric and semi-symmetric 3-valent graphs of small order (with Pll); Gl-graphs (with Pll); Regular maps on surfaces (with PI7); Regular and chiral maps with Leemans. o implementation of algorithms in Magma kernel, study of specific groups and related abstract polytopes, various enumeration and generation algorithms for groups, abstract polytopes, apartments and coset geometries., o Investigation of arc-types of vertex-transitive graphs (with Pll); new discoveries about half-arc-transitive graphs (with Pll and PI6); investigation of regular maps with nilpotent automorphism groups (with PI7); construction of chiral maps of all possible types (with PI7). AP2-Fowler o Progress on single-molecule conduction. Short note on the conducting properties of fullerenes (conductivity). Relationships between the various graph theoretical conjugated circuit models. New purely graph theoretical models of quantum mechanical approaches to distortion used by chemists and physicists (Jahn-Teller graphs), o Elected to Royal Society, citation included work on graph-theoretical modelling of currents, o New classification by nullity of omni-conductors and insulators. Chemical counterexamples for conjugated-circuit theory. AP3-lmrich o Attended CSASC 2011 in Krems, SODO 2012, CSD 6, CSASC 2013 and LL 2014 networking activities. Published book together with PI Klavzar. Work on recognition of products and near products (AP Leydold, PlsStadler, Klavzar) AP4-Klin o IN 2012 spent 3 weeks at Slovakia. Worked with Gyurki (from PI7). Discovery of families of certain association schemes by using computation algebra. o AP5-Schulte o Work on chiral polytopes and graph representations of abstract polytopes. 2. Scientific highlights (c.400-750 words) a. Describe the scientific highlights and main achievements of the CRP. What has been the most significant/valuable contribution to knowledge (e.g. results, breakthroughs)? PL-Pisanski • Professor Pisanski elected into Academia Europeae, published a book on Configurations. • Encyclopedia of graphs released (http://atlas.gregas.eu/) • Database of cubic vertex transitive graphs up to 1280 vertices generated. • The journal Ars Mathematica Contemporanea indexed by SCI since 2011 (IF=0,4) • Classification and characterization: equivelar 4-toroids, generalized Petersen as unit-distance graphs, Edge-transitive maps of small genus. G-laterals of certaion configurations. Medial symmetry maps. • Applications: Type graphs in chemistry. Graph theory and Jahn-Teller theorem. Strong traces introduced in synthetic biology, Map representation of DNA. Complex web side organization. PI2-Batagelj • New algorithms for network analysis implemented (in new libraries: net.Plexor, TQ, lanus) • 3 papers on bibliographic network analysis • Received INSNA's William D. Richards Jr., Software Award (2013) for Pajek PI3-Biyikoglu • Progress on minimum algebraic connectivity, AGX-system conjecture • Proved: polymeric molecules dendrimers have maximum spectral radius among all chemical trees • New algorithms: power allocation and partner selection polices problems in wireless, de novo sequencing, constrained alignment framework for the comparative analysis of a pair of metabolic pathways • Proved: rigorous relationship between several graph invariants, including entropy, Randic index and degree assortativity. • Graph model for multi party off-the-record communication • Spectral bounds for maximum induced matching PI4-Klavzar • An upper bound for the number of convex cycles in a given graph derived. Equality holds if and only if the graph is an even cycle or a Moore graph. • Proved that the Wiener index of a weighted graph can be expressed as the sum of the Wiener indices of weighted quotient graphs with respect to an arbitrary combination of Djokovic-Winkler-classes. Cut method can be used to compute an arbitrary distance moment of graphs isometrically embeddable into Cartesian products oftriangles. PI5-Klobucar • Several applications ofgraph theory in chemistry, bioinformatics, optimization, organization and analysis of communication networks, etc. 17 articles published in journals, 1 article in a book. • Generalised network descriptors were investigated • Network organization, network analysis and information protection were investigated PI6-Marusic • Classified cubic symmetric tricirculants, tetracirculants and automorphism groups of rational circulant graphs; Bicyclic graphs with extremal values of PI index. • Characterized tetravalent one regular graphs of order p2, symmetric Tabačjn graphs, pentavalent act-transitive bicirculants, half-arc transitive graphs with small alternets, cubic-symentric tri- and penta-circulants. • Prestigious publication in Proc. Lond. Math. Soc on Hamilton Cycles of Cayley graphs. • Several new results related to: connectivity of bipartite distance-balanced graphs, identifiable subgraphs, equistable graphs, threshold and domishold graphs, square roots of graphs, CIS circulants, claw freeness, domination. PI7-Škoviera • Classification and enumeration of 2-groups that factorise as a product of two cyclic groups with application on regular embeddings of bipartite graph. • Classification of various classes of regular maps • Construction: infinite classes or regular maps that are both self-dual and self-Petrie-dual • Asymptotic formulas for counting oriented and the number of reflexible maps • Matching numbers of intersection graphs of bases is characterized. • Optimal acyclic edge-colourings of cubic graphs are described. • Progress towards 6-decompositions of snarks. PI8-Stadler • An explicit construction of a minimum cycle bases for the lexicographic product of graphs. • Application of redundant non-invertible encodings in hard combinatorial optimization problems • An efficient heuristic for constructing alternative local multiple sequence alignments from a collection of local pairwise alignments developed, tested. • Retracts of Cartesian products of chordal graphs characterized. • Uniqueness of prime factorization of thin hypergraphs w.r.t. strong products has been proved and factorization algorithm is given. API Conder • Significant progress in generation and counting, of small regular polytopes, symmetric 3-valent graphs, regular maps and regular and special classes of chiral polytopes, regular Cayley maps for cyclic groups. Building several abstract polytope atlases. • Construction of special families maps, half-arc transitive graphs, symetric regular covers of kaleidoscopic regular maps with trinity symmetry • Algorithms, local s-transitivity in Magma, finding appartments in coset geometries, • Conder selected by the American and New Zealand Mathematical Societies as the first Maclaurin Lecturer, given the title of Distinguished Professor at the University of Auckland, and elected a Fellow of the American Mathematical Society AP2-Fowler • Elected as a Fellow of the Royal Society (FRS). • Established the mathematical background for definition of omniconducting graphs, chemical applications, conducting properties of fullerenes • Successful use of purely graph theoretical models in quantum mechanical approaches • Use of symmetry and graph theory for framework rigidity in engineering structures AP3-lmrich • book published : Handbook of product graphs • elected as a member ofAcademia Europea, section Informatics AP4-Klin • 4 new infinite families of non-Schurian association schemes on 2p2 vertices, p an odd prime • new infinite family of non-Schurian association schemes with 3 classes, which are invariant with respect to a suitable transitive action of groups PSL(2,q), q isa prime-power. AP5-Schulte • proved algebraic and combinatorial conditions for a polytope P that ensure action of automorphism on k-arcs of medial layer graph is transitive. Example families provide. b. List up to five of your CRP's most significant joint publications (i.e. involving co-authors from at least two IPs in your CRP or co-authors from other CRPs in the programme). 1. *Cabello S., Chimani M., Hlineny P., Computing the stretch of an embedded graph. SIAM journal on discrete mathematics, ISSN 0895-4801, 2014, vol. 28, no. 3, str. 1391-1401 2. *Biyikoglu, Turker and Leydold, Josef,Dendrimers are the unique chemical trees with maximum spectral radius. MATCH 68(2012), 851-854. 3. *Sergio Cabello, Jean Cardinal, Stefan Langerman, The Clique Problem in Ray Intersection Graphs, Algorithms - ESA 2012, Lecture Notes in Computer Science Volume 7501, 2012, pp 241-252 4. *Conder, Marston and Nedela, Roman and Siran, Jozef, Classification of regular maps of Euler characteristic $-3p$.J. Combin. Theory Ser. B 102 (2012), 967-981. http://dx.doi.Org/10.1016/j.jctb.2011.ll.003 5. *S.Majstorovic, D.Stevanovic „A note on graphs whose largest eigenvalues of the modularity matrix equals zero", Electronic Journal of Linear Algebra vol 27, 256 (2014) B.2. Integration of the CRP in the programme (300-600 words) 1. Describe the contribution of your CRP to the EUROCORES programme. What was the place and role of the CRP in the framework of the programme? From a scientific perspective, how well integrated was your CRP in the programme? How would you describe the intensity of interaction between your CRP and other CRPs in the programme? Our impression is that CRPs collaborate well. Networking events contributed to this the most. GReGAS CRP is established on the basis of long term EU and worldwide cooperation established around Slovenian, Austrian and Slovak graph theory cores. The coherence of the related network is based on strong personal and long term research relationships and periodic series of the conferences (every four years) with International conference of graph theory in Bled (Slovenia) GEMS workshops (Slovak Republic), SODO series (New Zealand) and other conferences filling the remaining year in the four year cycle held in different places (USA, Portugal, Mexico). Strong connections between Austrian and Slovenian groups are kept through Ljubljana-Leoben seminar every year. Establishing the scientific journal Ars Mathematica Contemporanea (founding editors and editors-in-chiefare PL Pisanski and PI Marušič) turned to be an important strategic decision, which have even strengthened the cooperation and brought it to the next level. GReGAS project is one of the first projects linking the parts of the network working on the common project goals. In the past and still on-going there were various smaller bilateral projects running between the different groups within the project. Members of our CRP have, through Slovak partners, a strong connection with Czech scientists and through this to the project GraDR. Thus GReGAS has relatively good cooperation established with leaders of GraDR, while connections with other two CRPs are weaker, but getting stronger especially through researchers working on crossing number and computational geometry. In such a setting the four CRPs represent four strong groups and EUROGIGA programme is an excellent choice to enhance cooperation between the groups. Motivated by various applications in sciences and technologies, the topics addressed in EUROGIGA call have high potential of establishing links with industry and other top sciences. Beside the strong scientific team, Slovenian GReGAS team involves also an industrial partner, Abelium company, which is a form of a spin-off from the group of PL Pisanski still keeping strong cooperation, but also rapidly developing in the industrial field. We believe that (possible) applications oftheory in technology represent the strong points of EUROGIGA related topics. We hope that the cooperation between groups in CRPs will lead to new project ideas through for application of Horizon 2020 projects. 2. Describe the benefit to your CRP of being part of the EUROCORES programme (e.g. achieving critical mass of expertise, scale and scope, visibility, collaborative opportunities, ideas, etc.). The main benefits of the EUROCORES programme is additional support for networking events which is an interesting concept providing enhancement mechanism for inter-project cooperation. CRPs itself contribute to better possibilities for work within the CRPs team. We can notice that exchange of young researchers (PhD students, post docs) and visits have increased. Networking events provide additional conferences and workshops "forcing" together different groups possibly providing "sparks" for new cooperation. So we absolutely support networking mechanisms and hope similar funds, especially for the biggest joint events could be provided in future. B.3. Cross-CRP networking, training and dissemination (max. 750 words) 1. Which networking/training/dissemination activities did you or your CRP members participate in? Indicate how many team members participated in each activity. Kick-off meeting, Paris: • 2 GReGAS members attended the event EuroGIGA Minisymposia at CSASC, 25-28 September 2011. Two minisymposia organized: • "Algebraic and topological graph theory", Organizers: Roman Nedela (Banska Bystrica), Tomasz Pisanksi (Ljubljana) - Organized by our CRP • "Combinatorics and Graph Theory", Organizers: Michael Drmota (Vienna), Jan Kratochvil (Prague), Marc Noy (Barcelona), Oriol Serra (Barcelona) o 9 GReGAS members attended the event SODO 2012 - Symmetries of Discrete Objects Conference and MAGMA Workshop, Queenstown, New Zealand, 13-17 February 2012: o 16 GReGAS members attended the event EuroGIGA Session in Assisi, on March 22, 2012, Assisi, Italy o 1 GReGAS members attended the event Eurogiga Midterm Conference, July 9-13, 2012, Prague, Czech Republic o 13 GReGAS members attended the event Computers in Scientific Discovery 6, August 21-25, Portorož, Slovenia o 25 GReGAS members attended the event CSASC Koper, 9-13 June, Koper, Slovenia o 24 GReGAS members attended the event o 3 out of 9 scientific minisimposia co-organised byGReGAS members EuroGIGA Final Conference in Berlin, February 17-21, 2014 o 11 GReGAS members attended the event EuroGIGA session at the GEMS workshop (Graph Embeddings and Maps on Surfaces), 14-19 July 2013, Smolenice, Slovakia o 11 GReGAS members attended the event Ljubljana-Leoben Graph Theory Seminar, 3-5 September, 2014, Koper, Slovenia o 15 GReGAS members attended the event 2. Networking activities. Describe the most important networking activity for your CRP (in terms of impact, outcome, creation of synergy and cooperation within or outside the programme). We believe that the most important networking activity was Conference of the Catalan, Slovenian, Austrian, Slovak and Czech mathematical societies, 9-13 June, Koper • Traditional conference organized every two years • 24 GReGAS members attended the event and members of all other EUROGIGA projects attended the conference as well • http://csasc2013.upr.si/ • 9 scientific, 1 educational and 1 EUROGIGA minisimposia • 108+ participants 3. Training activities. Describe the most useful training activity to date (workshop, course, school, etc.) undertaken by senior or junior researchers ofyour CRP. o Within SODO 2012 a Magma workshop was organized. o Two-week Summer school, "Topics in Algebraic graph theory" (Banska Bystrica, Slovakia), o PhD Summer School in Discrete Mathematics and Symmetries of Graphs and Networks III (Rogla, Slovenia) o PhD Summer School in Discrete Mathematics, Rogla, Slovenia /16-21 June 2013 o 2014 PhD Summer School in Discrete Mathematics, Rogla, Slovenia / 29 June - 5 July 2014 4. Dissemination activities. Describe the most valuable dissemination activity (or activities) your team undertook, with respect to (i) the scientific community and (ii) the wider public. Describe the outcome and impact of these activities in terms of promoting your field of research and the EUROCORES programme. Organisation or co-organisation of events: • 7th Slovenian International Conference on Graph Theory, Bled, Slovenia, 19 - 25 June 2011 • Meeting "Mathematics and Art", Ljubljana, Slovenija, junij, 2011 • Annual meeting of International academy for mathematical chemistry, Bled, Slovenija, junij 2011 • CSASC 2011, Krems Austria, T. Pisanski, R. Nedela chairing "Algebraic and topological graph theory" session. Also organization of EUROGIGA session. • SODO 2012, Symmetries of Discrete Objects, Conference and MAGMA Workshop, Queenstown, New Zealand, 13-17 February 2012 • Computers in Scientific Discovery (CSD) conference: CSD6 August 2012, Portorož, SI. This meeting had participants from chemistry, mathematics & computer science, with a strong representation from GREGAS researchers, and invited speakers included Nobel Laureate Sir Harold Kroto, whose seminal work on fullerenes is central to our theme of using graph theoretical ideas in chemical applications. • Joint Mathematical Conference CSASC 2013, 9.-13. 6. 2013 in Koper, Slovenia. • Graph Embeddings and Maps on Surfaces, GEMS 2014, Smolenice, Slovakia, 14.-19. 7. 2013 (organizers: Nedela, Skoviera, member of program committee: Siran, organization: Mačaj, Karabaš, Kotrbčik; Siran, Skoviera are are the editors of the special issue of Ars Mathematica Contemporanea) • 7th Czech-Slovak International Symposium on Graph Theory, Combinatorics, Algorithms and Applications, organized in Košice, 7-13.7. 2013 (Nedela, Skoviera - members of program committee; Skoviera - editor of special issue of Discrete Mathematics) • EuroComb 2013, Pisa, Italy, 9.-13. 9. 2013, program committee member: Skoviera • 7th Cracow Conference on Graph Theory "Rytro '14", partnered through the Standard Grant of the Visegrad Fund: Skoviera • 6th International Workshop on Optimal Network Topologies IWONT 2014, 30. 6. -4. 7. 2014, Bratislava, Slovakia, main organizers: Jajcay and Siran • Working retreat of the research team, 10.12.-14.12. 2014, MosonmagyarUv-r, Hungary. Organizer: Skoviera • Adriatic Conference on Graph Theory and Complexity, Split, Croatia, 25-27 April 2014. • ATCAGC 2013: Algebraic, Topological and Complexity Aspects of Graph Covers, Bovec, Slovenia / 28 January -1 February 2013 • DM |=60: I DM |=60 International Conference on Graph Theory and Combinatorics, dedicated to Prof. Dragan Marušič's 60th Birthday, Koper, Slovenia /1-3 May 2013 • Joint Workshop of Math Departments UP 1AM and UP FAMNIT, Rogla, Slovenia /17-19 May 2013 • Conference on Geometry: Theory and Applications, Ljubljana, Slovenia /24-28 June 2013 • 2nd Annual Mississippi Discrete Mathematics Workshop, Starkville, USA / 2 November 2013 • SYGN IV: Symmetries of Graphs and Networks IV, Rogla, Slovenia / 29 June - 5 July 2014 Associate partners • Royal Society Workshop: Symmetry, Rigidity & Periodicity in Natural & Engineered Structures, Chicheley Hall, Feb. 2012 (P. W. Fowler, initiator and co-organizer) • Aromaticity, International Conference on Physical Organic Chemistry (ICP0C21), Durham Sept, 2012 (P. W. Fowler, co-organizer) 5. List the cross-CRP activities your CRP organised or co-organised. EuroGIGA Minisympoisa at CSASC, 25-28 September 2011. GReGAS PL Pisanski and PI Nedela organized one of two EuroGIGA minisymposia: • "Algebraic and topological graph theory", Organizers: Roman Nedela (Banska Bystrica), Tomasz Pisanksi (Ljubljana) - Organized by our CRP • "Combinatorics and Graph Theory", Organizers: Michael Drmota (Vienna), Jan Kratochvil (Prague), Marc Noy (Barcelona), Oriol Serra (Barcelona) o 43 participants, o Organizers: GReGAS + GraDR o web: http://www.dmg.tuwien.ac.at/OMG/OMG-Tagung/ SODO 2012 - Symmetries of Discrete Objects Conference and MAGMA Workshop, Queenstown, New Zealand, 13-17 February 2012: o 67 Participants, o Organizers: GReGAS + GraDR o web: http://www.math.auckland.ac.nz/~conder/SODO-2012/ Computers in Scientific Discovery 6, August 21-25, Portorož, Slovenia o Scientific committee: Tomaž Pisanski (chair), Patrick Fowler, Klavdija Kutnar. o Organizing committee: Klavdija Kutnar (chair), Boštjan Frelih, Ademir Hujdurović, Alen o Organizers:GReGAS + ComPose CSASC Koper, 9-13 June, Koper, Slovenia • T. Pisanski, J. Kratochvil, R. Nedela - members of national scientific committees • Organizing committee: K. Kutnar, A. Orbanić, T. Pisanski, J. Prezelj • 3 out of 9 minisimposia coorganized by GReGAS members • Eurogiga minisimposium held • Organized by all EUROGIGA projects GEMS workshop (Graph Embeddings and Maps on Surfaces), 14-19 July 2013, Smolenice, Slovakia • main organizers: Nedela, Škoviera, in cooperation with GraDR • GReGAS members of program committee: Siran, • organization: Mačaj, Karabaš, Kotrbčik Ljubljana-Leoben Graph Theory Seminar, 3-5 September, 2014, Koper, Slovenia • GReGAS members of scientific committee: Imrich W., Klavžar S., Kutnar K., Pisanski T. • GReGAS members of organizing committee: Brešar B., Jakovac M., Kelenc A., Milanič M. B.4. Publications, dissemination and outreach Important: In your lists, include only those publications which resulted to a significant extent from work undertaken in theframework of the CRP or from collaboration with other CRPs. Note that ail such publications should bear an acknowledgement ofthe EuroGIGA programme. In addition: - List ail authors. - identify with an asterisk (*) publications which acknowledge the EUROCORES programme. - Underline publications/presentations involving co-authors from at least two IPs within your CRP. - Mark in bold publications/presentations involving co-authors from other CRPs in the programme. Publications - Articles Peer-reviewed articles injournals (published, in press orsubmitted) PL Pisanski Bauer, Andrej,On the failure of fixed-point theorems for chain-complete.Theoret. Comput. Sei. 430 (2012), 4350. http://dx.doi.Org/10.1016/j.tcs.2011.12.005 Horvat, Boris and Pisanski, Tomaz and Zitnik, Isomorphism Checking of l-graphs.Graphs Combin. 28 (2012), 823— 830. http://dx.doi.org/10.1007/s00373-011-1086-2 *Zitnik, Arjana and Horvat, Boris and Pisanski, All generalized Petersen graphs are unit-distance graphs.J. Korean Math. Soc. 49 (2012), 475-491. http://dx.doi.Org/10.4134/JKMS.2012.49.3.475 Horvat, Boris and Pisanski, Tomaz, Unit distance representations ofthe Petersen graph in the. Ars Combin. 104 (2012), 393-415. A. Ceulemans, E. Lijnen, P.W. Fowler, R.B. Mallion, T. Pisanski : S5 graphs as model systems for icosahedral JahnTeller problems, Theor. Chem. Acc. 131 (2012) Art 1246. DOI: 10.1007/00214-012-1246-3 Brinkmann, Gunnar, Van Cleemput, Nico, Pisanski, Tomaž. Generation ofvarious classes of trivalent graphs. Theor. comput. sei.. [Print ed.], 2012, 29 str. http://dx.doi.Org/10.1016/j.tcs.2012.01.018, doi: 10.1016/j.tcs.2012.01.018. Horvat, Boris and Kratochvil, Jan and Pisanski, Tomaž. On the computational complexity of degenerate unit distance representations of graphs, in Combinatorial algorithms, Lecture Notes in Comput. Sei. Vol. 6460. Springer, Heidelberg, 2011, 274-285 *Jaklič, Gašper and Juttler, Bert and Krajnc, Marjeta and Vitrih, Vito and Žagar, Emil. Hermite interpolation by rational $GAk$ motions of low.J. Comput. Appl. Math. 240 (2013), 20--30. http://dx.doi.Org/10.1016/j.cam.2012.08.021 Jaklic, Gasper and Kanduc, Tadej and, Energy Minimizing Mountain Ascent.J. Optim. Theory Appl. 155 (2012), 680-693. http://dx.doi.org/10.1007/sl0957-012-0088-4 Jaklic, Gasper and Modic, Jolanda, A note on "Methods for constructing distance matrices and the inverse eigenvalue problem".Linear Algebra Appl. 437 (2012), 2781-2792. http://dx.doi.Org/10.1016/j.laa.2012.06.044 Jaklic, Gasper and Kozak, Jernej and Krajnc, Marjeta and Vitrih, Vito and Zagar, Emil, An approach to geometric interpolation by Pythagorean-hodograph curves.Adv. Comput. Math. 37 (2012), 123-150. http://dx.doi.org/10.1007/sl0444-011-92Q9-0_ Jaklic, Gasper and Kozak, Jernej and Vitrih, Vito and Zagar, Emil, Lagrange geometric interpolation by rational spatial cubic Bezier curves.Comput. Aided Geom. Design 29 (2012), 175—188. http://dx.doi.Org/10.1016/j.cagd.2012.01.002 Jaklic, Gasper and Fowler, Patrick W. and Pisanski, Tomaz, HL-index of a graph. Ars Math. Contemp. 5 (2012), 99— 105. Jaklic, Gasper and Zagar, Emil, Curvature variation minimizing cubic Hermite interpolants.Appl. Math. Comput. 218 (2011), 3918-3924. http://dx.doi.Org/10.1016/j.amc.2011.09.039 Konvalinka, Matjaž, On quantum immanants and the cycle basis of the quantum permutation space.Ann. Comb. 16 (2012), 289-304. http://dx.doi.org/10.1007/s00026-012-0132-y Konvalinka, Matjaž, Skew quantum Murnaghan-Nakayama rule.J. Algebraic Combin. 35 (2012), 519-545. http://dx.doi.org/10.1007/sl0801-011-0312-6 Ciocan-Fontanine, lonut and Konvalinka, Matjaž and Pak, Igor, Quantum cohomology of $\rm Hilb_n(\Bbb Сл2)$ and the.J. Algebra 349 (2012), 268-283. http://dx.doi.Org/10.1016/j.jalgebra.2011.10.011 *Hubard, Isabel and Orbanic, Alen and Pellicer, Daniel and Ivic Weiss, Asia, Symmetries of Equivelar 4-Toroids.Discrete Comput. Geom. 48 (2012), 1110-1136. http://dx.doi.org/10.1007/s00454-012-9444-2 *0rbanic, Alen and Pellicer, Daniel and Pisanski, Tomaz and Tucker, Thomas W., Edge-transitive maps of low genus. Ars Math. Contemp. 4 (2011), 385-402. Pisanski, Tomaz and Balaban, Alexandru T., Flag graphs and their applications in mathematical chemistry for benzenoids.J. Math. Chem. 50 (2012), 893-903. http://dx.doi.org/10.1007/sl0910-011-9932-2 Gheorghiu, C. I. and Höchstenbach, M. E. and Plestenjak, B. and Rommes, J., Spectral collocation solutions to multiparameter Mathieu's system. Appl. Math. Comput. 218 (2012), 11990-12000. http://dx.doi.Org/10.1016/j.amc.2012.05.068 Knor, Martin and Potočnik, Primož, Efficient domination in cubic vertex-transitive graphs. European J. Combin. 33 (2012), 1755-1764. http://dx.doi.Org/10.1016/j.ejc.2012.04.007 A. Ceulemans, E. Lijnen, P.W. Fowler, R.B. Mallion, T. Pisanski : Graph Theory and the Jahn-Teller theorem, Proc. Ri A 468 (2012) 971-989. DOI: 10.1098/rspa.2011.0508 Cabello, Sergio, Many distances in planar graphs.Algorithmica 62 (2012), 361—381. http://dx.doi.org/10.1007/s00453-010-9459-0 *Sergio Cabello, Hardness ofApproximation for Crossing Number, Discrete & Computational Geometry, http://dx.doi.org/10.1007/s00454-012-9440-6 *Sergio Cabello, Jean Cardinal, Stefan Langerman, The Clique Problem in Ray Intersection Graphs, Algorithms -ESA 2012, Lecture Notes in Computer Science Volume 7501, 2012, pp 241-252 Jaklič G., Kanduč T., On positivity of principal minors of bivariate Bezier collocation matrix. Applied mathematics andcomputation, ISSN 0096-3003. [Print ed.], 2014, vol. 227, p. 320-328. Jaklič G., Modic J., Euclidean graph distance matrices of generalizations of the star graph. Applied mathematics andcomputation, ISSN 0096-3003. [Print ed.], 2014, vol. 230, p. 650-663. Kovač B. Žagar E., Emil. Some new G[sup]l quartic parametric approximants of circular arcs. Applied mathematics and computation, ISSN 0096-3003. [Print ed.], 2014, vol. 239, p. 254-264. *Gevay G., Pisanski T., Kronecker covers, V-construction, unit-distance graphs and isometric point-circle configurations. Ars mathematica contemporanea, 2014, vol. 7, no. 2, p. 317-336. Potočnik P., Wilson S., Linking Rings Structures and tetravalent semisymmetric graphs. Ars mathematica contemporanea, ISSN 1855-3966, 2014, vol. 7, no. 2, p. 341-352 KozakJ., Krajnc M., Vitrih V.. Dual representation ofspatial rational Pythagorean-hodograph curves. Computer AidedGeometricDesign, ISSN 0167-8396.,2014, vol. 31, no. 1, p. 43-56. Basti B., Bizzarri M., Ferjančič K., Kovač B., Krajnc M., Lavička M., Michälkova K., Šfr Z., Žagar E. C [sup] 2 Hermite interpolation by Pythagorean-hodograph quintic triarcs. ComputerAided Geometric Design, 2014, vol. 31, no. 78, p. 412-426. Knor M., Potočnik P., Škrekovski R., Relationship between the edge-Wiener index and the Gutman index ofa graph. Discrete appliedmathematics, 2014, vol. 167, p. 197-201. Knor M., Potočnik P., Škrekovski R., Complete solution of equation W(L[sup]3(T)) = W(T) for the Wiener index of iterated line graphs oftrees. Discrete applied mathematics, 2014, vol. 171, p. 90-103. Potočnik P., Tetravalent arc-transitive locally-Klein graphs with long consistent cycles. Europeanjournal of combinatorics, vol. 36, p. 270-281. *Knor M., Mačaj M., Potočnik P., Škrekovski R., Trees T satisfying W(L[sup]3(T)) = W(T). Filomat, ISSN 0354-5180, 2014, vol. 28, no. 3, p. 551-556. *Conder M. D. E., Pisanski T., Žitnik A., Gl-graphs: a new class ofgraphs with many symmetries. Journal of algebraiccombinatorics, 2014, vol. 40, issue 1, p. 209-231. Giudici M., Potočnik P., Verret G., Semiregular automorphisms of edge-transitive graphs. Journal ofalgebraic combinatorics, ISSN 0925-9899, 2014, vol. 40, iss. 4, p. 961-972. *Koike Quintanar S. H., Kovacs I., Pisanski T., The number of cyclic configurations of type (v_3) and the isomorphism problem. Journal ofcombinatorial designs, 2014, vol. 22, issue 5, p. 216-229, Košmrlj G., Realizations of the game domination number. Journal ofcombinatorial optimization, 2014, vol. 28, iss. 2, p. 447-461. Konvalinka M., Pak I., Cayley compositions, partitions, polytopes, and geometric bijections. Journal of combinatorial theory. SeriesA, 2014, vol. 123, iss. 1, p. 86-91. Terwilliger P., Žitnik A., Distance-regular graphs of q-Racah type and the universal Askey-Wilson algebra. Journal ofcombinatorial theory. SeriesA, 2014, vol. 125, p. 98-112. Potočnik P., Spiga P., Verret G., Bounding the order ofthe vertex-stabiliser in 3-valent vertex-transitive and 4-valent arc-transitive graphs. Journal ofcombinatorial theory. Series B, 2014, vol., iss., 33 pages. Krajnc M., Počkaj K., Vitrih V., Construction of low degree rational motions. Journal ofComputational and Applied Mathematics, 2014, vol. 256, p. 92-103. Basti B., Bizzarri M., Krajnc M., Lavička M., Michälkova K., Šfr Z., Vitrih V., Žagar E., C [sup] 1 Hermite interpolation with spatial Pythagorean-hodograph cubic biarcs. Journal ofComputational andApplied Mathematics, 2014, vol. 257, str. 65-78 *Horvat B., Jaklič G., Kavkler I., Randić M., Rank of Hadamard powers of Euclidean distance matrices. Journal of mathematical chemistry, 2014, vol. 52, iss. 2, p. 729-740. Muhič A., Plestenjak B., A method for computing all values [lambda] such that A + [lambda]B has a multiple eigenvalue. LinearAlgebra and itsApplications, 2014, vol. 440, p. 345-359. *Fijavž G., Pisanski T., RusJ., Strong traces model of self-assembly polypeptide structures. MATCH Communications in Mathematical and in Computer Chemistry, 2014, vol. 71, no. 1, p. 199-212. *Kovič i., Pisanski T., Balaban A. T., Fowler, P. W. On symmetries of benzenoid systems. MATCH Communications in Mathematical and in ComputerChemistry, 2014, vol. 72, no. 1, p. 3-26. *Boros E., Heggernes, P., Van 'T Hof P., Milanič M., Vector connectivity in graphs. Networks, 2014, vol. 63, issue 4, p. 277-285. *Cabello S., Chimani M., Hlineny P., Computing the stretch of an embedded graph. SIAM journal on discrete mathematics, ISSN 0895-4801, 2014, vol. 28, no. 3, str. 1391-1401. Potočnik P., Spiga P., Verret G., On the order of arc-stabilisers in arc-transitive graphs with prescribed local group. Transactions oftheAmerican MathematicalSociety, 2014, vol. 366, no. 7, p. 3729-3745. Konvalinka M., Pak I., Triangulations ofCayley and Tutte polytopes. Advances in mathematics, 2013, vol. 245, str. 1-33. Knor M., Potočnik P., Škrekovski R., Wiener index of iterated line graphs oftrees homeomorphic to the claw K [sub] {1,3}. Ars mathematica contemporanea, 2013, vol. 6, no. 2, p. 211-219. Andova V., Knor M., Potočnik P., Škrekovski R., On a variation of Randič index. Australasianjournal of combinatorics, 2013, vol. 56, p. 61-75. Boben M., Grünbaum B., Pisanski T., Multilateral in configurations. Beiträge zurAlgebra und Geometrie, ISSN 0138-4821, 2013, vol. 54, iss. 1, p. 263-275. Jaklič G., Modic J., Inverse eigenvalue problem for Euclidean distance matrices ofsize 3. Bulletin oftheAustralian Mathematical Society, 2013, vol. 87, iss. 1, p. 82-93. *Cabello S., Diaz-Banez, J. M., Perez Lantero, P., Covering a bichromatic point set with two disjoint monochromatic disks. Computational geometry, 2013, vol. 46, iss. 3, p. 203-212. Jaklič G., Sampoli M. L., Šestini A., Žagar E., C [sup] 1 rational interpolation of spherical motions with rational rotation-minimizing directed frames. ComputerAided GeometricDesign, 2013, vol. 30, iss. 1, p. 159-173. Jaklič G., Kozak J., Krajnc M., Vitrih V., Žagar E., High order parametric polynomial approximation of conic sections. Constructive approximation, 2013, vol. 38, iss. 1, p. 1-18. *Randič M., Horvat B., Jaklič G., Plavšič D., Pisanski T., On map representations of DNA. Croatica chemica acta, 2013, vol. 86, no. 4, p. 519-529. *Cabello S., Hardness ofapproximation for crossing number. Discrete & computational geometry, ISSN 01795376, 2013, vol. 49, iss. 2, p. 348-358. *Cabello S., Cardinal J., Langerman S., The clique problem in ray intersection graphs. Discrete & computational geometry, 2013, vol. 50, iss. 3, p. 771-783. Knor M., Potočnik P., Škrekovski R., Wiener index of iterated line graphs oftrees homeomorphic to H. Discrete Mathematics, ISSN 0012-365X. [Print ed.], 2013, vol. 313, iss. 10, p. 1104-1111. http://dx.doi.Org/10.1016/j.disc.2013.02.005. *Hubard I., del Rio Francos M., Orbanić A., Pisanski T., Medial symmetry type graphs. The Electronicjournal of combinatorics, 2013, vol. 20, iss. 3, p 29 (38 pages.). Dolžan D., Konvalinka M., Oblak P., Diameters of connected components of commuting graphs. The electronic journal oflinear algebra, 2013, vol. 26, p. 433-445. Jaklič G., Modic J., On Euclidean distance matrices of graphs. The electronicjournal oflinear algebra, 2013, vol. 26, p. 574-589. Bauer A., Cvetko-Vah K., Stone duality for skew Boolean algebras with intersections. Houston journal of mathematics, 2013, vol. 39, no. 1, p. 73-109. Konvalinka M., Lauve A., Skew Pieri rules for Hall-Littlewood functions. Journal ofalgebraic combinatorics, 2013, vol. 38, iss. 3, p. 499-518. Potočnik P., Locally arc-transitive graphs ofvalence {3,4} with trivial edge kernel. Journal ofalgebraic combinatorics, 2013, vol. 38, iss. 3, p. 637-651. Cvetko-Vah K., Leech J., Spinks M., Skew lattices and binary operations on functions. Journal ofapplied logic, 2013, vol. 11, iss. 3, p. 253-265. Jaklič G., Jüttler B., Krajnc M., Vitrih V., Žagar E., Hermite interpolation by rational G [sup] k motions of low degree. Journal ofComputational andApplied Mathematics, 2013, vol. 240, p. 20-30. *Pisanski J., Pisanski T., Žumer M., A new approach to complex web site organization : Jan Pisanski, Tomaz [i. e. Tomaž] Pisanski and Maja Zumer [i. e. Žumer]. Journal ofinformation science, 2013, 39, 6, p. 805-814. Potočnik P., Spiga P., Verret G., Cubic vertex-transitive graphs on up to 1280 vertices. Journal ofsymbolic computation, 2013, vol. 50, p. 465-477. Milanič M., Pisanski T., Žitnik A., Dilation coefficient, plane-width, and resolution coefficient of graphs. MonatsheftefürMathematik, 2013, vol. 170, no. 2, p. 179-193. Cabello S., Chambers E. W., Erickson J., Multiple-source shortest paths in embedded graphs. SIAM journal on computing, 2013, vol. 42, no. 4, p. 1542-1571. Cabello S., Mohar B., Adding one edge to planar graphs makes crossing number and 1-planarity hard. SIAM journal on computing, 2013, vol. 42, iss. 5, p. 1803-1829. *Brinkmann, Gunnar, Van Cleemput, Nico, Pisanski, Tomaž. Generation ofvarious classes oftrivalent graphs. Theoretical computerscience, 2013, vol. 502, p. 16-29. PI Batagelj Breznik, K, Batagelj, V: Retired matches among male professional tennis players, Journal of Sports Science and Medicine (2012), Volume 11, Issue 2, 270-278. http://www.jssm.org/volll/n2/10/vlln2-10pdf.pdf Gomez-Nünez A. J., Batagelj V., Vargas-Quesada B., de Moya-Anegon F., Chinchilla-Rodriguez, 1., Optimizing SCImago Journal & Country Rank classification by community detection. Journal ofinformetrics, 2014, vol. 8, iss. 2, p. 369-383. *Bodlaj J., Batagelj V., Network analysis of publications on topological indices from the Web ofScience. Molecular informatics, 2014, vol. 33, iss. 8, p. 514-535. *Cerinšek M., Batagelj V., Network analysis ofZentralblatt MATH data. Scientometrics, 2014, 25 pages. *Batagelj V., Cerinšek M., On bibliographic networks. Scientometrics, 2013, vol. 96, iss. 3, p. 845-864. PI Biyikoglu Biyikoglu, Turker and Leydold, Josef,Graphs of given order and size and minimum algebraic.Linear Algebra Appl. 436(2012), 2067-2077. http://dx.doi.Org/10.1016/j.laa.2011.09.026 *Biyikoglu, Turker and Leydold, Josef,Dendrimers are the unique chemical trees with maximum spectral radius. MATCH 68(2012), 851-854. F. Alkan, T. Biyikoglu, M. Demange and C. Erten, Constrained Alignments of a Pair ofGraphs, submitted (2014). *G. Abaka, T. Biyikoglu, C. Erten, CAMPways: constrained alignment framework for the comparative analysis of a pair of metabolic pathways, Bioinformatics, 29: 145-153 (2013). PI Klavžar llic, Aleksandar and Klavzar, Sandi and Rho, Yoomi, The index of a binary word. Theoret. Comput. Sei. 452 (2012), 100-106. http://dx.doi.Org/10.1016/j.tcs.2012.05.025 llic, Aleksandar and Klavzar, Sandi and Rho, Yoomi, Generalized Lucas cubes.Appl. Anal. Discrete Math. 6 (2012), 82-94. http://dx.doi.org/10.2298/AADM 1201080021 * Klavzar, Sandi and Mollard, Michel, Cube polynomial of Fibonacci and Lucas cubes. Acta Appl. Math. 117 (2012), 93-105. http://dx.doi.org/10.1007/sl0440-011-9652-4 Anand, Bijo S. and Changat, Manoj and Klav\vzar, Sandi and Peterin, Iztok, Convex sets in lexicographic products of graphs. Graphs Combin. 28 (2012), 77-84. http://dx.doi.org/10.1007/s00373-011-1031-4 Bresar, Boštjan and Kovse, Matjaž and, Geodetic sets in graphs.Structural analysis of complex networks , Birkhauser/Springer, NewYork, 2011, 197-218. http://dx.doi.org/10.1007/978-0-8176-4789-6_8 *Klavzar, Sandi and Peterin, Iztok and Žemljic, Sara Sabrina, Hamming dimension of a graph—The case of Sierpinski graphs, European J. Combin. 34 (2013) 460-473 *Klavzar, Sandi and Nadjafi-Arani, M.J., Wiener index in weighted graphsvia unification of $\ThetaA\ast$-classes, European J. Combin. 34 (2014) 71-76. *J. Azarija, S. Klavžar, Moore graphs and cycles are extremal graphs for convex cycles, J. Graph Theory, to appear, DOI: 10.1002/jgt.21837. *D. Bokal, M. Chimani, J. Leanos, Crossing number additivity over edge cuts, European J. Combin. 34 (2013) 1010-1018. http://dx.doi.Org/10.1016/j.ejc.2013.02.002 *A.M. Hinz, S. Klavžar, S.S. Zemljič, Sierpinski graphs as spanning subgraphs of Hanoi graphs, Appl. Anal. Discrete Math. 7 (2013) 72-82. http://link.springer.com/article/10.2478/sll533-013-Q227-7 *M. Jakovac, A. Taranenko, On the k-path vertex cover of some graph products, Discrete Math. 313 (2013) 94100. http://dx.doi.Org/10.1016/j.disc.2012.09.010 M. Jakovac, I. Peterin, The b-chromatic index ofa graph, Bull. Malays. Math. Sei. Soc., to appear. *S. Klavžar, Structure of Fibonacci cubes: a survey, J. Comb. Optim. 25 (2013) 505-522. http://dx.doi.org/10.1007/slQ878-011-9433-z *S. Klavžar, M. Mollard, Asymptotic properties of Fibonacci cubes and Lucas cubes, Ann. Comb. 18 (2014) 447457. http://dx.doi.org/10.1007/s00026-014-Q233-x *S. Klavžar, M.J. Nadjafi-Arani, Wiener index in weighted graphs via unification of 0*-classes, European J. Combin. 36 (2014) 71-76. http://dx.doi.Org/10.1016/j.ejc.2013.04.008 *S. Klavžar, M.J. Nadjafi-Arani, Improved bounds on the difference between the Szeged index and the Wiener index ofgraphs, European J. Combin. 39 (2014) 148-156. http://dx.doi.Org/10.1016/j.ejc.2014.01.005 *S. Klavžar, M.J. Nadjafi-Arani, Computing distance moments on graphs with transitive Djokovid-Winkler's relation, Discrete Appl. Math. 166 (2014) 269-272. http://dx.doi.Org/10.1016/j.dam.2013.10.006 *S. Klavžar, Y. Rho, Fibonacci (p,r)-cubes as Cartesian products, Discrete Math. 328 (2014) 23-26. http://dx.doi.Org/10.1016/j.disc.2014.03.027 *S. Klavžar, Y. Rho, On the Wiener index ofgeneralized Fibonacci cubes and Lucas cubes, submitted. *S. Klavžar, S.S. Zemljič, On distances in Sierpinski graphs: almost-extreme vertices and metric dimension, Appl. Anal. Discrete Math. 7 (2013) 72-82. http://dx.doi.org/10.2298/AADM130109Q01K, http://pefmath.etf.rs/vol7numl/AADM-Vol7-Nol-72-82.pdf Z. Shao, A. Vesel, L(2,l)-labeling ofthe strong product of paths and cycles, Sei. World J. (2014) Article ID 741932, 12 pages, http://dx.doi.org/10.1155/2014/741932 D. Korže, A. Vesel, On the packing chromatic number of square and hexagonal lattice. Ars Math. Contemp. 7 (2014) 13-22. http://amc-journal.eu/index.php/amc/article/view/255/224 Z. Shao, A. Vesel, A note on the chromatic number ofthe square ofthe Cartesian product oftwo cycles, Discrete Math. 313 (2013) 999-1001. http://dx.doi.Org/10.1016/j.disc.2013.01.025 *Z. Shao, A. Vesel, L(3,2,l)-labeling of triangular and toroidal grids, to appear in Cent. European J. Oper. Res., DOI 10.1007/sl0100-014-0365-4. *A. Taranenko, A new characterization and a recognition algorithm of Lucas cubes, Discrete Math. Theor. Comput. Sci. 15(3) (2013) 31-39. http://www.dmtcs.org/dmtcs-ojs/index.php/dmtcs/article/view/2192/4357. *I.G. Yero, M. Jakovac, D. Kuziak, The security number of strong grid-like graphs, submitted. *I.G. Yero, M. Jakovac, D. Kuziak, A. Taranenko, The partition dimension of strong product graphs and Cartesian product graphs. Discrete Math. 331 (2014) 43-52. http://dx.doi.Org/10.1016/j.disc.2014.04.026 PI Klobučar Furtula Boris, Gutman Ivan, Ivanovic Milos and Vukicevic Damir, Computer search for trees with minimal ABC index, Applied Mathematics and Computation, Vol. 219 (2012), No.2, 767-772 Vukicevic Damir, Gutman Ivan, Furtula Boris, Andova Vesna and Dimitrov Darko, Some observations on comparing Zagreb indices", MATCH. Communications in Mathematical and in Computer Chemistry, Vol. 66 (2011), No.2, 627-645 Sedlar Jelena, "The global forcing number of the parallelogram polyhex", Discrete Applied Mathematics. The Journal ofCombinatorial Algorithms, Informatics and Computational Sciences, Vol. 160 (2012), No.15, 23062313 Doslic Tomislav, Furtula Boris, Graovac Ante, Gutman Ivan, Moradi Sirous and Yarahmadi Zahra, "On vertex-degree-based molecular structure descriptors", Communications in Mathematical and in Computer Chemistry, Vol.66 (2011), No.2, 613-626 *Majstorović Snjezana, Doslic Tomislav and Klobučar Antoaneta, "K-domination on Hexagonal Catus Chains", Kragujevac Journal of Mathematics, Vol.36 (2012), No.2, 335-347 Randic Milan, Vukicevic Damir, Novic Marjana et al., "pi-Electron Currents in Larger Fully Aromatic Benzenoids", INTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Vol.112 (2012), No.12, 2456-2462 Randic Milan, Vukicevic Damir, Balaban Alexandru T. et al., "Conjugated circuits currents in hexabenzocoronene and itsderivativesformed by joiningproximal carbons",JOURNALOFCOMPUTATIONALCHEMISTRY,Vol.33 (2012), No.ll, 1111-1122 Randic Milan, Novic Marjana, Vracko Marjan, Vukicevic Damir et al., "pi-electron currents in polycyclic conjugated hydrocarbons: Coronene and its isomers having five and seven member rings", INTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Vol.112 (2012), No.4, 972-985 *Caporossi Gilles, Paiva Marcia, Vukicevic Damir et al., "Centrality and Betweenness: Vertex and Edge Decomposition ofthe Wiener Index", MATCH-COMMUNICATIONS IN MATHEMATICAL AND IN COMPUTER CHEMISTRY, Vol.68 (2012), No.l, 293-302_ Vukicevic Damir, Durdevic Jelena and Gutman, Ivan, "Limitations of Pauling Bond Order Concept", POLYCYCLIC AROMATIC COMPOUNDS, Vol.32 (2012), No.l, 36-47 Vukicevic Damir and Durdevic Jelena, "Bond additive modeling 10. Upper and lower bounds of bond incident degree indices ofcatacondensed fluoranthenes", CHEMICAL PHYSICS LETTERS, Vol.515 (2011), No.1-3, 186-189 Sedlar Jelena, Vukicevic Damirand Hansen Pierre, "Using size for bounding expressions of graph invariants", Annals of Operations Research, Vol.188 (2011), 415-427 Vukicevic Damir, "Bond additive modeling 6. Randomness vs. design", MATCH. Communications in Mathematical and in Computer Chemistry, Vol.65 (2011), No.2, 415-426 Vukicevic Damir, "Chor coefficient—measuring correlation in chemistry", MATCH. Communications in Mathematical and in Computer Chemistry, Vol.65 (2011), No.2, 365-382 *Sedlar Jelena, "On augmented eccentric connectivity index of graphs and trees", MATCH : communications in mathematical and in computer chemistry, Vol.68 (2012), No. 2, 325-342 Fath-Tabar G. H., Vaez-Zadeh B., Ashrafi A. R. and Graovac, A.,"Some inequalities for the atom-bond connectivity index ofgraph operations", Discrete Applied Mathematics. The Journal ofCombinatorial Algorithms, Informatics and Computational Sciences, Vol.159 (2011), No.13, 1323-1330 Doslic Tomislav, Graovac Ante and Ori Ottorino, "Eccentric connectivity index of hexagonal belts and chains", MATCH. Communications in Mathematical and in Computer Chemistry, Vol.65 (2011), No.3, 745-752 *Komech Nedia, Vukičević Damir, Ladram Ali; et al. "Improving the Selectivity ofAntimicrobial Peptides from Anuran Skin", Journal of Chemical Information and Modeling, Volume: 52, Issue: 12 (2012); 3341-3351 *S. Antunović, T. Kokan, T. Vojković and D. Vukičević "Generalised network descriptors", (211-230), Glasnik Matematički, Vol. 48, No.2 (2013) *Sedlar, Jelena; Vukičević, Damir; Cataldo, Franco; Ori, Ottorino; Graovac, Ante. "Compression ratio ofWiener index in 2-d rectangular and polygonal lattices", Ars mathematica contemporanea. 7 (2014); 1-12. *A.KIobučar, I.Puljić, „Some results for Roman domination number on cardinal products of paths and cycles", Kragujevac Journal of Mathematics, Vol. 38, No.l (2014) *J.Sedlar "Remoteness, proximity and few other distance invariants in graphs" Filomat 27:8 (2013), 1425-1435. *S.Majstorovic, D.Stevanovic „A note on graphs whose largest eigenvalues of the modularity matrix equals zero", Electronic Journal of Linear Algebra vol 27, 256 (2014) *S. Majstorović, G. Caporossi, "Bounds and relations involving the adjusted centrality of a tree", Graphs and Combinatorics (accepted for publication) PI Marušič Araluze, Alexander and Kovacs, Istvan and Kutnar, Klavdija and Martinez, Luis and Marusic, Dragan, Partial sum quadruples and bi-Abelian digraphs.J. Combin. Theory Ser. A 119 (2012), 1811-1831. http://dx.doi.Org/10.1016/j.jcta.2012.06.004 Kovacs, Istvan and Kutnar, Klavdija and, Classification of cubic symmetric tricirculants.Electron. J. Combin. 19 (2012), Paper 24, 14. Klin, Mikhail and Kovacs, Istvan, Automorphism groups of rational circulant graphs. Electron. J. Combin. 19 (2012), Paper 35, 52._ Glover, Henry H. and Kutnar, Klavdija and Malni\vc, Hamilton cycles in (2, odd, 3)-Cayleygraphs.Proc. Lond. Math. Soc. (3) 104 (2012), 1171-1197. http://dx.doi.org/10.1112/plms/pdr042 Miklavič, Štefko and Spari, Primož, On the connectivity of bipartite distance-balanced graphs.European J. Combin. 33 (2012), 237-247. http://dx.doi.Org/10.1016/j.ejc.2011.10.002 *Kaminski, Marcin and Medvedev, Paul and Milanic, Martin, Complexity of independent set reconfigurability problems. Theoret. Comput. Sei. 439 (2012), 9-15. http://dx.doi.Org/10.1016/j.tcs.2012.03.004 Frelih, Boštjan and Kutnar, Klavdija, Classification of cubic symmetric tetracirculants and.European J. Combin. 34 (2013), 169-194. http://dx.doi.Org/10.1016/j.ejc.2012.08.005 Vukicevic, Zana Kovijanic and Stevanovic, Dragan, Bicyclic graphs with extremal values of PI index.Discrete Appl. Math. 161 (2013), 395-403. http://dx.doi.Org/10.1016/j.dam.2012.09.015 Krajnc, Marjeta and Vitrih, Vito, Motion design with Euler-Rodrigues frames of quintic.Math. Comput. Simulation 82 (2012), 1696-1711. http://dx.doi.Org/10.1016/j.matcom.2012.04.003 Pasalic, E. and Zhang, W. G., On multiple output bent functions.lnform. Process. Lett. 112 (2012), 811-815. http://dx.doi.Org/10.1016/j.ipl.2012.07.009 *Levit, V. E., Milanič M. Equistable simplicial, very well covered, and line graphs. V: FAIGLE, Ulrich (ur.), NICOSIA, Gaia (ur.), PACIFICI, Andrea (ur.). 10th Cologne/Twente Workshop on Graphs and Combinatorial Optimization (CTW2011), (Discrete applied mathematics, ISSN 0166-218X, Vol. 165). Amsterdam: Elsevier, 2014, p. 205-212, *Koike Quintanar S. H., Koväcs I., Isomorphic tetravalent cyclic Haar graphs. V: Bled'll - 7th Slovenian International Conference on Graph Theory, 19-25 June 2011, Bled, Slovenia. Ars mathematica contemporanea : special issue Bled'll, (Ars mathematica contemporanea, ISSN 1855-3966, Vol. 7, no. 1, 2014). Ljubljana: DM FA Slovenije, 2014, p. 215-235. Bhoumik S., Dobson E., Morris J., On the automorphism groups of almost all circulant graphs and digraphs. V: Bled'll - 7th Slovenian International Conference on Graph Theory, 19-25 June 2011, Bled, Slovenia. Ars mathematica contemporanea : special issue Bled'll, (Ars mathematica contemporanea, Vol. 7, no. 2, 2014). Ljubljana: DMFA Slovenije, 2014, p. 487-506 Kaminski M., Milanič M., On the complexity ofthe identifiable subgraph problem. Discrete applied mathematics, ISSN 0166-218X. [Print ed.], 2014, p. 1-9. *Chiarelli N., Milanič M., On a class of graphs between threshold and total domishold graphs. Discrete applied mathematics, ISSN 0166-218X. [Print ed.], 2014, p. 1-16. *Milanič M., Oversberg A., Schaudt O., A characterization of line graphs that are squares of graphs. Discrete applied mathematics, 2014, vol. 173, p. 83-91. *Milanič M., Tomescu A. I., Set graphs. IV, Further connections with claw-freeness. Discrete applied mathematics, 2014, vol. 174, str. 113-121. *Boros E., Gurvich V., Milanič M., On CIS circulants. Discrete Mathematics, ISSN 0012-365X. [Print ed.], 2014, vol. 318, p. 78-95. Dobson E., Koväcs I., Miklavič Š., The isomorphism problem for rose window graphs. Discrete Mathematics, 2014, vol. 323, p. 7-13 *Milanič M., Pedersen A. S., Pellicer D., Verret G., Graphs whose complement and square are isomorphic. Discrete Mathematics, 2014, vol. 327, p. 62-75. *Brešar B., GolograncT., Milanič M., Rail D. F., Rizzi R., Dominating sequences in graphs. Discrete Mathematics, ISSN 0012-365X. [Print ed.], 2014, vol. 336, str. 22-36. Dobson E., On the Cayley isomorphism problem for Cayley objects of nilpotent groups of some orders. The Electronicjournal ofcombinatorics, 2014, vol. 21, no. 3, p3.8 (15 pages.). Kutnar K., Miklavič Š., Nicely distance-balanced graphs. Europeanjournal ofcombinatorics, ISSN 0195-6698, 2014, vol. 39, iss. 1, p. 57-67. Feng Y-Q, Kutnar K., Marušič D., Zhang C. Tetravalent one-regular graphs of order 4p [sup] 2. Filomat, 2014, vol. 28, no. 2, p. 285-303. Koväcs I., RuffJ., Integral automorphisms of affine planes over finite fields. Finitefields and their applications, ISSN 1071-5797, 2014, vol. 27, p. 104-114. *Arroyo A., Hubard I., Kutnar K., O'Reilly E., Šparl P., Classification of symmetric Tabačjn graphs. Graphs and combinatorics, 2014, vol. 30, is., 17 pages. *Lozin V.V., Milanič M., Purcell C., Graphs without large apples and the maximum weight independent set problem. Graphs andcombinatorics, ISSN 0911-0119, 2014, vol. 30, issue 2, p. 395-410. Kutnar K., Marušič D., Shi J., Zhang C., Finite groups with some non-cyclic subgroups having small indices in their normalizes. Journal ofalgebra andits applications, 2013, vol. 13, no. 4, p. 1350141-1-1350141-6. *Antončič I., Hujdurović A., Kutnar K.. A classification of pentavalent arc-transitive bicirculants. Journal of algebraiccombinatorics, 2014, vol., is., 26 pages., *Hujdurovič A., Kutnar K., Marušič D., Half-arc-transitive graphs with small number of alternets. Journal of combinatorial theory. SeriesA, 2014, vol. 124, iss. 2, p. 114-129, doi: Miklavič Š., Šparl P., On distance-regular Cayley graphs on abelian groups. Journal ofcombinatorial theory. Series B, 2014, vol. 108, p. 102-122. Koväcs, Istvän. Covering systems of direct products of elementary p-groups are regular. Acta scientiarum mathematicarum, 2013, vol. 79, no. 1-2, p. 31-41. Evdokimov S., Koväcs I., Ponomarenko I., Characterization of cyclic Schur groups. Algebra i analiz, 2013, torn. 25, n 5, p. 61-85. Lin, C-K, Teng, Y-H., Tan J. J. M., Hsu L-H., Marušič D., The spanning laceability on the faulty bipartite hypercube-like networks. Applied mathematics and computation, 2013, vol. 219, iss. 15, p. 8095-8103. *Milanič M., A note on domination and independence-domination numbers ofgraphs. V: Bled'll - 7th Slovenian International Conference on Graph Theory, 19-25 June 2011, Bled, Slovenia. Ars mathematica contemporanea : specialissue Bled'll, (Ars mathematica contemporanea, Vol. 6, no. 1, 2013). Ljubljana: DMFA Slovenije, 2013, vol. 6, no. 1, p. 89-97. Miklavič Š., A note on a conjecture on consistent cycles. Ars mathematica contemporanea, 2013, vol. 6, no. 2, p. 389-392. *Heggernes P., Van 'T Hof P., Milanič M., Induced subtrees in interval graphs. V: 24th International Workshop, IWOCA 2013, Rouen, France, July 10-12, 2013. LECROQ, Thierry (ur.), MOUCHARD, Laurent (ur.). Combinatorial algorithms : 24th International Workshop, IWOCA 2013, Rouen, France, July 10-12, 2013 : revisedselected papers, (Lecture notes in computer science, 8288). Berlin: Springer, 2013, p. 230-243 *Cicalese F., Milanič M., Vaccaro U., On the approximability and exact algorithms for vector domination and related problems in graphs. Discrete applied mathematics, 2013, vol. 161, iss. 6, p. 750-767. *Milanič M., Schaudt O., Computing square roots of trivially perfect and threshold graphs. Discrete applied mathematics, ISSN 0166-218X. [Print ed.], 2013, vol. 161, no. 10/11, p. 1538-1545. Frelih B., Miklavič Š., Edge regular graph products. The Electronicjournal ofcombinatorics, 2013, vol. 20, no. 1, p. 62 (17 pages.). *Lozin V. V., Milanič M., Critical properties ofgraphs of bounded clique-width. Discrete Mathematics, 2013, vol. 313, issue 9, p. 1035-1044. Frelih B., Kutnar K., Classification ofcubic symmetric tetracirculants and pentacirculants. Europeanjournal of combinatorics, 2013, vol. 34, iss. 2, p. 169-194 *Kutnar K., Marušič D., Miklavič Š., Strašek R., Automorphism groups ofTabačjn graphs. Filomat, 2013, vol. 27, no. 7, p. 1157-1164. *Hujdurovič A., Kutnar K., Marušič D., On prime-valent symmetric bicirculants and Cayley snarks. V: Nielsen Frank (ed.), Barbaresco Frederic (ed.). Geometricscience ofinformation : 1st International Conference, GSI 2013, Paris, France, August 28-30, 2013 : proceedings, (Lecture notes in computer science, 8085). Berlin: Springer, 2013, p. 196-203. *Chiarelli N., Milanič M., Linear separation of total dominating sets in graphs. V: WG 2013, 39th International Workshop on Graph-Theoretic Concepts in Computer Science, June 19 - 21, 2013, Lübeck, Germany. BRANDSTÄDT, Andreas (ur.), JANSEN, Klaus (ur.), REISCHUK, Rüdiger (ur.). Graph-theoreticconceptsin computer science : 39th International Workshop, WG 2013, Lübeck, Germany, June 19-21, 2013 : revised papers, (Lecture notes in computer science, ISSN 0302-9743, 8165). Heidelberg [etc.]: Springer, cop. 2013, p. 165-176. Miklavič Š., On bipartite distance-regular graphs with intersection numbers $c_i$=$(qAi-l)/(q-l)$. Graphs and combinatorics, 2013, vol. 29, iss. 1, p. 121-130. Koväcs I., Arc-transitiv dihedrants ofodd prime-power order. Graphs and combinatorics, 2013, vol. 29, issue 3, p. 569-583. *Kutnar K., Marušič D., Šparl P., Wang R-J., Xu M-Y. Classification of half-arc-transitive graphs of order 4p. Europeanjournal ofcombinatorics, 2013, vol. 34, iss. 7, p. 1158-1176. Miklavič Š., Terwilliger P., Bipartite Q-polynomial distance-regular graphs and uniform posets. Journal of algebraiccombinatorics, 2013, vol. 38, iss. 2, p. 225-242. Koväcs I., Marušič D., Muzychuk M., On G-arc-regular dihedrants and regular dihedral maps. Journal ofalgebraic combinatorics, 2013, vol. 38, issue 2, p. 437-455. Anholcer M., Cichacz S., Milanič M., Group irregularity strength of connected graphs. Journal ofcombinatorial optimization, 2013, p. 1-17. Kutnar K., Malnič A., Martinez L., Marušič D., Quasi m-Cayley strongly regular graphs. Journal ofthe Korean Mathematical Society, ISSN 0304-9914, 2013, vol. 50, no. 6, str. 1199-1211. Cicalese F., Cordasco G., Gargano L., Milanič M., Vaccaro U., Latency-bounded target set selection in social networks. V: e9th Conference on Computability in Europe, CiE 2013, Milan, Italy, July 1-5, 2013. Bonizzoni Paola (ed.), Brattka Vasco (ed.), Löwe Benedikt (ed.). The nature ofcomputation : logic, algorithms, applications : 9th Conference on Computability in Europe, CiE 2013, Milan, Italy, July 1-5, 2013 : proceedings, (Lecture notes in computer science, ISSN 0302-9743, 7921). Heidelberg [etc.]: Springer, cop. 2013, p. 65-77. Brandstädt A., Milanič M., Nevries R., New polynomial cases ofthe weighted efficient domination problem. V: Chatterjee Krishnendu (ed.), Sgall Jiri (ed.). Mathematicalfoundations of computerscience 2013 : 38th International Symposium, MFCS 2013, Klosterneuburg, Austria, August 26-30, 2013 : proceedings, (Lecture notes in computer science, ISSN 0302-9743, 8087). Berlin: Springer, 2013, p. 195-206. Fritzilas E., Milanič M., Monnot J, Rios-Solis, Y. A. Resilience and optimization of identifiable bipartite graphs. V: Demange Marc (ur.), et al. Seventh International Conference on Graphs and Optimization, (Discrete applied mathematics, ISSN 0166-218X, Vol. 161, iss. 4/5). Amsterdam: Elsevier, 2013, p. 593-603. Milanič M., Tomescu A. I. Set graphs. I. Hereditarily finite sets and extensional acyclic orientations. V: DEMANGE, Marc (ur.), et al. Seventh International Conference on Graphs and Optimization, (Discrete applied mathematics, ISSN 0166-218X, Vol. 161, iss. 4/5). Amsterdam: Elsevier, 2013, p. 677-690. *Boros E., Heggernes P., Van 'T Hof P., Milanič M.,Vector connectivity in graphs. V: 10th International Conference, TAM C 2013, Hong Kong, China, May 20-22, 2013. Chan Hubert T. H. (ed.), Lau Lap Chi (ed.), Trevisan, Luca (ed.). Theory and applications ofmodels ofcomputation : 10th International Conference, TAMC 2013, Hong Kong, China, May20-22, 2013 : proceedings, (Lecture notes in computer science, ISSN 0302-9743, 7876). Heidelberg [etc.]: Springer, cop. 2013, p. 331-342. PI Skoviera *Du, Shaofei and Jones, Gareth and Kwak, Jin Ho and Nedela, Roman and Skoviera, Martin, 2-groups that factorise as products of cyclic groups, and regular embeddings of complete bipartite graphs.Ars Math. Contemp. 6 (2013), 155-170. Lukotka, R. and Macajova, E. and Mazak, J. and Skoviera, M., Circuits of length 5 in 2-factors of cubic graphs.Discrete Math. 312 (2012), 2131-2134. http://dx.doi.Org/10.1016/j.disc.2011.05.026 Rollova, Edita and Skoviera, Martin, Nowhere-zero flows in Cartesian bundles of graphs.European J. Combin. 33 (2012), 867-871. http://dx.doi.Org/10.1016/j.ejc.2011.09.022 *Kotrbcik, Michal and Skoviera, Martin, Matchings, cycle bases, and the maximum genus ofa graph.Electron. J. Combin. 19 (2012), РарегЗ, 12. Grannell, Mike J. and Griggs, Terry S. and Macajova, Edita and Skoviera, Martin, Coloring Cubic Graphs by PointIntransitive SteinerTriple Systems, in press, http://dx.doi.org/10.1002/jgt.21698 *Karabas, Jan and Macajova, Edita and Nedela, Roman, 6-decomposition of snarks. European J. Combin. 34 (2013), 111-122. http://dx.doi.Org/10.1016/j.ejc.2012.07.019 *Conder, Marston and Nedela, Roman and Siran, Jozef, Classification of regular maps of Euler characteristic $-3p$.J. Combin. Theory Ser. B 102 (2012), 967-981. http://dx.doi.Org/10.1016/j.jctb.2011.ll.003 Kotrbcik, Michal, A note on disjoint cycles.lnform. Process. Lett. 112 (2012), 135-137. http://dx.doi.Org/10.1016/j.ipl.2011.ll.006 *Jones, Gareth A. and Macaj, Martin and Siran, Jozef, Nonorientable regular maps over linear fractional groups. Ars Math. Contemp. 6 (2013), 25-35. Siagiova, Jana and Siran, Jozef, Covalence sequences oftransitive plane tessellations and. Australas. J. Combin. 53 (2012), 171-178. *Andersen, Lars Dovling and Macajova, Edita and Mazak, Jan, Optimal acyclic edge-coloring of cubic graphs.Journal ofGraph Theory 71 (2012), 353-364. http://dx.doi.org/10.1002/jgt.20650 Macajova, Edita and Mazak, Jan, An Algorithm for Optimal Acyclic Edge-Colouring of Cubic Graphs.Frontiers in Algorithmics and Algorithmic Aspects in Information and Management Lecture Notes in Computer Science (6681), Springer Berlin Heidelberg, 2011, 136-146. http://dx.doi.org/10.1007/978-3-642-21204-8_17 *Djidjev, Hristo N. and Vrto, Imrich, Planar Crossing Numbers ofGraphs of Bounded Genus.Discrete & Computational Geometry48 (2012), 393-415. http://dx.doi.org/10.1007/s00454-012-9430-8 *S.-F. Du, G. Jones, J. H. Kwak, R. Nedela, M. Škoviera, 2-Groups that factorise as products of cyclic groups, and regular embeddings of complete bipartite graphs, Ars Mathematica Contemporanea 6 (2013), 155nl70. *G. A. Jones, M. Mačaj, J. Siran: Nonorientable regular maps over linear fractional groups, Ars Mathematica Contemporanea 6 (2013), 25-35. *M. J. Grannell, T. S. Griggs, E. Mačajova, M. Škoviera: Coloring cubic graphs by point-intransitive Steiner triple systems, Journal of Graph Theory 74 (2013), 163-181. *M. Mačaj, J. Mazak: Asymptotic lower bounds on circular chromatic index of snarks, Electronic Journal of Combinatorics 20 (2013), #P2. *G. Exoo, R. Jajcay, J. Širan: Cayley cages, Journal ofAlgebraic Combinatorics 38 (2013), 209-224. J. Širan: How symmetric can maps on surfaces be?, Surveys in Combinatorics, London Mathematical Society Lecture Note Series 409, Cambridge University Press, 2013, 161-238. *L. Faria, C. M.H. de Figueiredo, R. Bruce Richter, I. Vrto: The same upper bound for both: the 2-page and the rectilinear crossing numbers ofthe n-cube, Proc. 39th Intl. Workshop on Graph-Theoretic Concepts in Computer Science, WG 2013, A. Brandstaedt et al. eds, Lecture Notes in Computer Science 8165, Springer, Berlin, 2013, 249-260. *J. Karabas E. Mačajova, R. Nedela: 6-Decomposition of snarks, European Journal of Combinatorics 34 (2013), 111-122. *R. Lukotka: Circular flow number ofgeneralized Blanusa snarks, Discrete Mathematics 313 (2013), 975n981 *R. Lukotka, E. Rollova: Flows on thejoin oftwo graphs, Mathematica Bohemica 138 (2013), 383n396. *E. Mačajova, J. Mazak: On even cycle decompositions of 4-regular line graphs, Discrete Mathematics 313 (2013), 1697-1699. *C. Balbuena, M. Miller, J. Širan, M.Ždimalova: Largevertex-transitive graphsofdiameter2from incidence graphs of biaffine planes, Discrete Mathematics 313 (2013), 2014-2019. *Š. Gyurki, J-n Mazak: An efficient algorithm for testing goal-minimality of graphs, Discrete Applied Mathematics 161 (2013), 1632-1634. E. Mačajova, M. Škoviera, Sparsely intersecting perfect matchings in cubic graphs, Combinatorica 34 (2014), 6194. *M. Knor, J. Širan, Smallestvertex-transitive graphs ofgiven degree and diameter, J. Graph Theory 75 (2014), 137-149. *K. Hu, R. Nedela, N.E. Wang, Classification of regular cyclic coverings of Platonic maps, European J. Combin. 36(2014), 531-549. PI Stadler Hellmuth, Marc and Ostermeier, Philipp-Jens and Stadler, Peter, Minimum cycle bases of lexicographic products.Ars Math. Contemp. 5 (2012), 219-230. *Hellmuth, Marc and Ostermeier, Lydia and Stadler, Peter F., A survey on hypergraph products.Math. Comput. Sei. 6 (2012), 1-32. http://dx.doi.org/10.1007/sll786-012-0109-6 Otto, Wolfgang and Stadler, Peter F. and Prohaska, Sonja J., Phylogenese footprinting and consistent sets of local.Combinatorial pattern matching Lecture Notes in Comput. Sei. (6661), Springer, 2011, 118—131. http://dx.doi.org/10.1007/978-3-642-21458-5_12 Long, Yangjing and Yang, Ling and Stadler, Peter F. and Jost, Jürgen, Relations Between Graphs, accepted Hellmuth, Marc and Leydold, Josef and Stadler, Peter F., Convex Cycle Bases.Acta Math. Contemp. (2011), . Brešar, Boštjan and Chalopin, Jeremie and Chepoi, Victor and Kovše, Matjaž and Labourel, Arnaud and Vaxs, Yann, Retracts of Products of Chordal Graphs, To appear: http://onlinelibrary.wiley.eom/doi/10.1002/jgt.21665/abstracthttp://dx.doi.org/10.1002/jgt.21665_ Foucaud, Florent and Kovse, Matjaž, Identifying path covers in graphs, submitted Foucaud, Florent and Kovse, Matjaž, On graph identification problems and the special case of identifying vertices using paths, To appear: http://www.springer.com/computer/theoretical+computer+science/book/978-3-642-35925-5 *Flamm, Christoph and Stadler, Barbel M. R. and, Generalized Topologies: hypergraphs, chemical reactions, and, submitted *Hellmuth, Marc and Ostermeier, Lydia and Stadler, Peter F., Square Property, Equitable Partitions, and Productlike, submitted *Hellmuth, Marc and Ostermeier, Lydia and Stadler, Peter F., Unique Square Property, Equitable Partitions, and Product-like Graphs, Discr. Math. 320 (2014) 92-103 *Ostermeier, Lydia and Stadler, Peter F., The Grid Property, and Product-like Hypergraphs, To appear: http://link.springer.com/article/10.1007/s00373-013-1392-y *Hellmuth, Marc and Noll, Manuel and Ostermeier, Lydia, Strong products of hypergraphs: Unique prime factorization theorems and algorithms, Discr. Appl. Math. 171 (2014) 60-71 *Hellmuth, Marc and Marc, Tilen and Ostermeier, Lydia and Stadler, Peter F., The Relaxed Square Property, submitted(2014) *Stadler, Barbel M. R. and Stadler, Peter F., Connectivity Spaces, submitted (2014) Associate Partners' main references Hartley, Michael I. and Hubard, Isabel and Leemans, Dimitri,Two atlases ofabstractchiral polytopesforsmall groups.Ars Math. Contemp. 5 (2012), 371-382. Conder, M. D. E., Archdeacon, D., & Siran, J. (2014). Trinity symmetry and kaleidoscopic regular maps. Transactions oftheAmerican Mathematical Society, 366, 4491-4512. W. Imrich and S. Klavžar, Two-ended regular median graphs, Discrete Math. 311 (2011), 1418- 1422 J. Cuno, W. Imrich, and F. Lehner, Distinguishing graphs with infinite motion and nonlinear growth, Ars Math. Contemp. 7 (2014), 201-213. M. Hellmuth, W. Imrich, and T. Kupka, Partial Star Products: A Local Covering Approach for the Recognition of Approximate Cartesian Product Graphs, Math. Comput. Sei. 7 (2013), 255 - 273. L. Sunil Chandran, Wilfried Imrich, Rogers Mathew, and Deepak Rajendraprasad, Boxicity and cubicity of product graphs, Graph Theory and Applications, 233—238, CRM Series, 16, Ed. Norm., Pisa, 2013 W. Imrich, R. Kalinowski, F. Lehner, and M. Pilsniak, Endomorphism Breaking in Graphs, E-JC, 21 (2114), #P1.16 R. Hammack and W. Imrich, Fast Recognition of Direct and Strong Products, Ars Math. Contemp., 8 (2015) 487497 W. Imrich, Simon M. Smith, Thomas W. Tucker, and Mark E. Watkins, Infinite motion and the distinguishing number ofgraphs and groups, J. Algebraic Comb., DOI 10.1007/sl0801-014-0529-2 M. Hellmuth, W. Imrich, and T. Kupka, Fast Recognition of Partial Star Products and Quasi Cartesian Products, Ars Math. Contemp., online December 2014 Tetiana Boiko, Johannes Cuno, Wilfried Imrich, Florian Lehner and Christiaan E. van de Woestijne, The Cartesian productofgraphswithloops, ArsMath.Contemp.,accepted October 2014 I. Sciriha, M. Debono, M. Borg, P.W. Fowler, B.T. Pickup: Interlacing-extremal graphs, Ars Mathematica Contemporanea 6 (2013) 261-278. Published on web: 19 November 2012, see http://amc.imfm.si/index.php/amc/article/view/275 P.W. Fowler, W. Myrvold, W.H. Bird: Counterexamples to a proposed algorithm for Fries structures of benzenoids, J. Math. Chem. 50 (2012) 2408-2426. DOI: 10.1007/sl0910-012-0039-l P.W. Fowler, M. Jooyandeh, G. Brinkmann: Face-spiral codes in cubic polyhedral graphs with face sizes no larger than six, J. Math. Chem. 50 (2012) 2272-2280. DOI: 10.1007/sl0910-012-0029-3 A. Ceulemans, E. Lijnen, P.W. Fowler, R.B. Mallion, T. Pisanski : Graph Theory and the Jahn-Teller theorem, Proc. Roy. Soc.A468 (2012) 971-989. DOI: 10.1098/rspa.2011.0508 P.W. Fowler, W. Myrvold: The 'anthracene problem': closed-form conjugated-circuit models of ring currents in linear polyacenes, J. Phys. Chem. A 115 (2011) 13191-13200. D0l:10.1021/jp206548t A. Soncini, P.W. Fowler: Visualising aromaticity of bowl-shaped molecules, Phys. Chem. Chem. Phys., 13 (2011), 20637 - 20643. P.W. Fowler, B.T. Pickup, T.Z. Todorova: A graph-theoretical model for ballistic conduction in single-molecule conductors, Pure Appl. Chem. 83 (2011) 1515-1528. P.W. Fowler, T. Pisanski: Golden graphs, Int. J. Chemical Modelling 3 (2011) 7-13. M. Dutour Sikirić, P. W. Fowler: Cubic polyhedral Ramanujan graphs with face size no larger than six, J. Math. Chem. 49 (2011) 843-858. P.W. Fowler: Möbius systems and the Estrada Index, MATCH Commun. Math. Comput. Chem. 66 (2011) 751-764. P. W. Fowler, S. Cotton, D. Jenkinson, W, Myrvold, W. H. Bird: Equiaromatic benzenoids: arbitrarily large sets of isomers with equal ring currents, Chem. Phys. Lett. 597 (2014) 30-35. DOI: 10.1016/j.cplett.2014.02.021 P. W. Fowler, B. T. Pickup, T.Z. Todorova, M. Borg, I. Sciriha: Omni-conducting and omni-insulating molecules, J. Chem. Phys. 140 (2014) 054115. DOI: 10.1063/1.4863559 P.W. Fowler, C. M. Gibson, D. E. Bean: Writing with ring currents: selectively hydrogenated polycyclic aromatics as finite models ofgraphene and graphane. Proc. Roy. Soc. A, 470 (2014) 20130617. DOI: 10.1098/rspa.2013.0617 J. Kovič, T. Pisanski, A.T. Balaban, P.W. Fowler: On symmetries of benzenoid systems, MATCH Commun. Math. Comput. Chem., 72 (2014) 3-26. P.W. Fowler, W. Myrvold: Most fullerenes have no centrosymmetric labelling, MATCH Commun. Math. Comput. Chem. 71 (2014) 93-97. W. Myrvold, P.W. Fowler: Fast Enumeration of All Independent Sets upto Isomorphism, Journal of Combinatorial Mathematics and Combinatorial Computing, 85 (2013) 173-194. P. W. Fowler, B. T. Pickup, T. Z. Todorova, R. De Los Reyes, I. Sciriha, Omni-conducting fullerenes, Chemical Physics Letters, 568 (2013) 33-35. doi:10.1016/j. cplett.2013.03.022 W. Oziminski, M. Palusiak, J. Dominkowska, T.M. Krygowski, R.W.A. Havenith, C.M. Gibson, P.W. Fowler: Capturing the elusive aromaticity of bicalicene, Phys Chem Chem Phys, 15 (2013), 3286-3293. doi:10.1039/c2cp43426a Mixer, Mark and Schulte, Egon, Symmetric Graphs from Polytopes of High Rank.Graphs Combin. 28 (2012), 843— 857. http://dx.doi.org/10.1007/s0Q373-011-1089-z_ Schulte, Egon and Wills, Jorg M., Convex-faced combinatorial^ regular polyhedra of small genus. Symmetry 4 (2012), 1-14. http://dx.doi.org/10.3390/sym4010001 E.Schulte, Polyhedra, complexes, nets and symmetry, Acta Crystallographica Section A 70 (2014), 203-216. G.Gevay, E.Schulte and J.M.Wills, The regular Grunbaum polyhedron ofgenus 5, Advances in Geometry 14 (2014), 465-482. D.Pellicer and E.Schulte, Polygonal complexes and graphs for crystallographic groups, In: Symmetry and Rigidity, (eds. R.Connelly, A.lvic Weiss and W.Whiteley), Fields Institute Communications, Vol. 20, Springer (New York, 2014), 325-344. M.Mixer, E.Schulte and A.lvic Weiss, Hereditary polytopes, In: Symmetry and Rigidity, (eds. R.Connelly, A.lvi\'{c} Weiss and W.Whiteley), Fields Institute Communications, Vol. 20, Springer (NewYork, 2014), 279-302. E.Schulte, Regular Polygonal Complexes of Higher Ranks in $\mathbb{E}A3$, Model. Anal. Inform. Sist. 20 (2013), 103-110. A.M.Cutler, E.Schulte and J.M.Wills, Icosahedral skeletal polyhedra realizing Petrie relatives of Gordan's regular map, Contributions to Algebra and Geometry 54 (2013), 651-657. G.Araujo-Pardo, I.Hubard, D.OIiveros and E.Schulte, Colorful polytopes and graphs, Israel Journal of Mathematics 195 (2013), 647-675. D.Pellicer and E.Schulte, Regular polygonal complexes in space, II (with D.Pellicer), Transactions American Mathematical Society 365 (2013), 2031-2061. M.Del Rio-Francos, I.Hubard, D.OIiveros and E.Schulte, Symmetric graphicahedra, Ars Mathematica Contemporanea 5 (2012), 383-405. Published contributions to international conferences МАТН/СНЕМ/СОМР 2011 (Dubrovnik) SedlarJelena, Vukičević Damir, RajtmajerSarah Michele, "On ordering alkanes by modified Zagreb indices", Split - Zagreb: Faculty ofSciences, University of Split; Hum naklada d.o.o., 2011. 38-38 Baksi, S. and Kaya, O. and Biyikoglu, T., Wireless Communications and Networking Conference (WCNC), 2012 IEEE. Optimal and near-optimal partner selection algorithms in cooperative OFDMA. 2012. 475 -479 Hell, Pavol; Imrich, Wilfried; Nesetril, Jaroslav Preface [Algebraic graph theory - a volume dedicated to Gert Sabidussi on the occasion ofhis 80th birthday]. Discrete Math. 312 (2012), 5-6 Cuno, Johannes; Imrich, Wilfried; Lehner, Florian. Distinguishing graphs with infinite motion andnonlinear growth, Ars Math. Contemp., accepted A.Kiefer, D. Leemans. On pairs of commuting involutions in Sym(n) and Alt(n), Comm. Algebra, to appear, J.De Saedeleer, D. Leemans, M. Mixer, T.Pisanski. Core-free, rank two coset geometries from edge-transitive bipartite graphs, Math. Slovaca, to appear M.-E. Fernandes, D. Leemans, M. Mixer. All alternating groups An with n >= 12 have polytopes of rank ?(n-l)/2?, SIAM Journal on Discrete Math. 26 (2012), nr. 2, 482-498; M.I.Hartley, I.Hubard, D. Leemans. Regular 4-polytopes from the Livingstone graph ofJanko's first group, J. Alg. Combi. 35 (2012), 193-214. M.-E.Fernandes, D. Leemans, M. Mixer. Polytopes of high rank for the alternating groups. J. Combin. Theory Ser. A 119 (2012), 42-56;_ M.-E.Fernandes, D. Leemans. Polytopes of high rank for the symmetric groups, Adv. Math. 228 (2011), 32073222; Leydold, Josef. 2012. Dendrimers are the unique chemical trees with maximum spectral radius. MATCH Communications in Mathematical and in Computer Chemistry 68 (3): 851-854. S. Baksi, O. Kaya and T. Biyikoglu, Enabling Cooperation, Resource Allocation and Receiver Selection Across Cells: Complementary Fractional Frequency Reuse. IEEE PIMRC 2013, London, UK, Sept. 2013. 1190-1195. Will, Sebastian and Stadler, Peter F., A Common Framework for Linear and Cyclic Multipe Sequence Alignment Problems. WABI 2014, Lect. Notes Comp. Sei 8701 (2014), 135-147. M. Kotrbčik, M. Škoviera: Locally-maximal embeddings ofgraphs in orientable surfaces, The Seventh European Conference on Combinatorics, Graph Theory and Applications EuroComb 2013, J. Neöetil et al. (eds.), CMR Series Vol. 16, Scuola Normale Superiore, Pisa, 2013,215-220. R. Lukotka, J. Mazak: Non-trivial snarks with given circular chromatic index, The Seventh European Conference on Combinatorics, Graph Theory and Applications EuroComb 2013, J. Neöefil et al. (eds.), CMR Series Vol. 16, Scuola Normale Superiore, Pisa, 2013, 65-70. R. Lukotka, J. Mazak and X. Zhu: Degenerated induced subgraphs of planar graph, The Seventh European Conference on Combinatorics, Graph Theory and Applications EuroComb 2013, J. Neöefil et al. (eds.), CMR Series Vol. 16, Scuola Normale Superiore Pisa, 2013, 259-264. R. Lukotka, E. Mačajova-, J. Mazak, M. Škoviera: Snarks with large oddness and small number ofvertices, The Seventh European Conference on Combinatorics, Graph Theory and Applications EuroComb 2013, J. Neöefil et al. (eds.), CMR Series Vol. 16, Scuola Normale Superiore Pisa, 2013, 59-64. News & Views-type articles / Other articles (please define) / - Books ^s editor(s) / As author(s) or author(s) ofchapters R. Nedela, M. Škoviera: Maps. Section 7.6 (42 pp.) in Handbook of Graph Theory, eds. J. Yellen, J. Gross, 2nd ed, in press. Pisanski, Tomaž, Servatius, Brigitte, Configurations from a Graphical Viewpoint, Birkhäuser Advanced Texts Basier Lehrbücher, Birkhäuser Basel. 2013, XIII, 279 p. 274 illus., 45 in color. Klemm, Konstantin and Stadler, Peter F., Theory and Principled Methods for Designing Metaheustics, Elementary Landscapes (Borenstein, Yossi and Moraglio, Alberto eds.). Springer, Berlin, 2013 in press. Bresar, Boštjan and Kovse, Matjaz and, Geodetic sets in graphs.Structural analysis of complex networks , Birkhauser Springer, NewYork, 2011, 197-218. http://dx.doi.org/10.1007/978-0-8176-4789-6_8 Vukicevic Damir, "Applications of perfect matchings in chemistry", Book:11 Structural analysis of complex networks", Birkhäuser/Springer, NewYork, 2011, Pages=463-482 Chapter: P.W. Fowler, A. Graovac: The Estrada Index and Fullerene Isomerism. Chapter 14, pp 265-280, In Mathematics and Topology of Fullerenes, Eds. F. Cataldo A. Graovac, O. Ori,, Carbon Materials: Chemistry and Physics 4 , Springer, New York, 2011. Cicalese, Ferdinando and Milanic, Martin and Vaccaro, Hardness, approximability, and exact algorithms for vector.Fundamentals of computation theory Lecture Notes in Comput. Sei. (6914), Springer, 2011, 288—297. http://dx.doi.org/10.1007/978-3-642-22953-4_25 Cicalese, Ferdinando and Milanic, Martin, Graphs of separability at most two: structural. Combinatorial algorithms Lecture Notes in Comput. Sei. (6460), Springer, 2011, 291-302. http://dx.doi.org/10.1007/978-3-642-19222-7_30 Kaminski, Marcin and Medvedev, Paul and Milani\vc, Shortest paths between shortest paths and independent sets.Combinatorial algorithms Lecture Notes in Comput. Sei. (6460), Springer, 2011, 56-67. http://dx.doi.org/10.1007/978-3-642-19222-7_7 Hammack, Richard and Imrich, Wilfried and Klavžar, Sandi, Handbook of product graphs, Second Edition. Discrete Mathematics and its Applications (Boca Raton). CRC Press. 2011 Klemm, Konstantin and Stadler, Peter F., Rugged and Elementary Landscapes. Theory and Principled Methods for the Design of Metaheuristics. (Borenstein Yossi and Moraglio, Alberto eds.), Springer, 2014, 41-46. Klemm, Konstantin and Qin, Jing and Stadler, Peter F., Geometry and coarse-grained representations of landscapes. Recent advances in the theory and application offitness landscapes. (Engelbrecht, Andries and Richter, Hendrik eds.), Springer, 2014, 153-176. Flamm, Christoph and Stadler, Barbel M.R. and Stadler, Peter F., Generalized Topologies: hypergraphs, chemical reactions, and biological evolution. Advances in Mathematical Chemistry: With applications to chemoinformatics, bioinformatics, drug discovery, and predictive toxicology. (Basak, Subash C. and Restrepo, Guillermo and Villaveces, Jose Luis eds.) Bentham, 2013, accepted R. Nedela, M. äkoviera, Maps, Chapter 7.6 in "Handbook of Graph Theory", J. L. Gross, J. Yellen, Eds., Chapman and Hall/CRC Press, December 2013, pp. 820-859 (Second Edition, 1630 pages), monograph chapter Batagelj, Vladimir, Mrvar, Andrej: Pajek. Alhajj, Reda, Rokne, Jon (Eds.) Encyclopedia ofSocial NetworkAnalysis and Mining. Springer, 2014, Vol. 2, M-R, 1245-1256. Cerinšek, Monika, Batagelj, Vladimir: Semirings and Matrix Analysis of Networks. Alhajj, Reda, Rokne, Jon (Eds.) Encyclopedia ofSocial NetworkAnalysisand Mining. Springer, 2014, Vol. 3, S-Z, 1681-1687. Cerinšek, Monika, Batagelj, Vladimir: Sources of Network Data. Alhajj, Reda, Rokne, Jon (Eds.) Encyclopedia of Social Network Analysis and Mining. Springer, 2014, Vol. 3, S-Z, 1946-1954. Orbanić, Alen: Tools for Networks. Alhajj, Reda, Rokne, Jon (Eds.) Encyclopedia ofSocial Network Analysis and Mining. Springer, 2014, Vol. 3, S-Z, 2166-2175. Bodlaj, Jernej. Network data file formats. Alhajj, Reda, Rokne, Jon (Eds.) Encyclopedia ofSocial Network Analysis and Mining. Springer, 2014, 1076-1091. - Other Please define (data products, video, etc.) • net.Plexor - will be collected from contributions (http://www.abelium.eu/development/net.plexor) • GReGAS Atlas - Encyclopedia ofGraphs (http://atlas.gregas.eu/) • Batagelj. V., A. Mrvar, A. WoS2Pajek 1.0 (October 2011). A program for transforming WoS data into corresponding Pajek networks. Python source http://pajek.imfm.si/lib/exe/fetch.php?media=dl:wos2pajekl0.zip • V. Batagelj. Preprint 0.3 (Jun 2012). A program for transforming citation networks with some small strong components into corresponding acyclic network. Python source: http://pajek.imfm.si/lib/exe/fetch.php?media=dl:preprint.py • V. Batagelj, lanus - Python tool for dynamic network analysis and visualization (http://pajek.imfm.si) • V. Batagelj, TQ - Python tool for temporal quantities (http://pajek.imfm.si) Presentations in scientific meetings - Oral presentations (indicate invited / keynote talks) 7th Slovenian International Conference on Graph Theory, Bled, Slovenia, June 2011 (majority of project members, invited speakers: Škoviera, Imrich, Schulte) T. Pisanski. Meeting "Mathematics and Art", Ljubljana, Slovenija, June 2011 T. Pisanski. Workshop on Symmetry in Graphs, Maps, and Polytopes, Toronto, Canada, October 2011 (invited speaker) T. Pisanski. The 35th Australasian Conference on Combinatorial Mathematics & Combinatorial Computing, Monash University, Melbourne, Australia, December 2011 Batagelj Vladimir, Cerinšek Monika, Horvat Boris: Network analysis of Zentralblatt MATH data. 7th Slovenian International Conference on Graph Theory, Jun 2011, Bled, Slovenia. Bodlaj Jernej, Batagelj Vladimir, Orbanić Alen: OpenGL® Graphical User Interface for net.Plexor - Interactive Large Network Analysis Library. 7th Slovenian International Conference on Graph Theory, Jun 2011, Bled, Slovenia. Batagelj Vladimir, Cerinšek Monika, Horvat Boris, Pisanski Tomaž: Exploring the structure of mathematical publications, CSASC 2011, September 2011, Krems, Austria. Batagelj Vladimir, Cerinšek Monika, Horvat Boris, Pisanski Tomaž: The structure of mathematics from Zentralblatt MATH data. 16th Young Statisticians Meeting, October 2011, Rijeka, Croatia. Batagelj Vladimir, Cerinšek Monika, Horvat Boris, Pisanski Tomaž: The structure of mathematics from the Zentralblatt MATH data base. Sunbelt XXXII, March 2012, Redondo Beach, CA, USA. Breznik Kristijan, Batagelj Vladimir: Network analysis of tennis games in the Open Era. Sunbelt XXXII, March 2012, Redondo Beach, CA, USA. Sandi Klavžar: Fibonacci cubes, generalized Fibonacci cubes, and bad words, invited plenary talk at Combinatorics 2012, Perugia, Italy, September 2012 (invited talk). Sandi Klavžar: Generalized Fibonacci cubes and three related problems on binary words, invited plenary talk at The 21st Workshop 3inl", Krakow, Poland, November 2012 (invited talk). Aleksander Vesel: Linear recognition and embedding of Fibonacci cubes, talk at Combinatorics 2012, Perugia, Italy, September 2012 (invited talk). Math Chem Comp, Dubrovnik (13.6.-18.6.2011) // Snjezana Majstorovic, Antoaneta Klobucar:K-domination on hexagonal chain cacti (talk) EuroGiga Midterm Conference, July 2012, Prague, Czech Republic // Snjezana Majstorovic: Domination on m-ary chain cacti (talk) 8th Meeting of the International Academy of Mathematical Chemistry, June 2012, Verona, Italy // Snjezana Majstorovic: Bounds and relations involving betweenness centrality in some families of graphs (talk) MATH/CHEM/COMP 2011 (Dubrovnik) //SedlarJelena, Vukičević Damir, RajtmajerSarah Michele, "On ordering alkanes by modified Zagreb indices" // 7th Slovenian International Conference on Graph Theory (Bled, 2011) //D. Vukičević, "Community detection in complex networks" Dragan Marušič, On two open problems in vertex-transitive graphs, "Beijing International Workshop on Group Actions on Combinatorial Structures", August 21 - 27, 2011, Beijing, China. (INVITED TALK). Klavdija Kutnar, Classification ofcubic symmetric polycirculants, "Beijing International Workshop on Group Actions on Combinatorial Structures", August21- 27, 2011, Beijing, China. (INVITED TALK). Edward Dobson, Which Johnson graphs and folded Johnson graphs are Cayley graphs, "Beijing International Workshop on Group Actions on Combinatorial Structures", August 21 - 27, 2011, Beijing, China. (INVITED TALK). Dragan Marušič, Searching for snarks amongst Cayley graphs, "CID 2011 Colourings, Independence and Domination 14th WORKSHOP ON GRAPH THEORY" September 18 - 23, 2011, Szklarska Poreba, Poland. Klavdija Kutnar, Cubic Cayley graphs and snarks, "Workshop on Symmetry in Graphs, Maps, and Polytopes", October 24-27, 2011, the Fields Institute, Toronto, Canada (INVITED TALK). Dragan Marušič, Half-arc-transitive graphs - possible research directions, "Workshop on Symmetry in Graphs, Maps, and Polytopes", October 24-27, 2011, the Fields Institute, Toronto, Canada. Aleksander Malnič, On the Split Structure of Lifted Groups, "Workshop on Symmetry in Graphs, Maps, and Polytopes", October 24-27, 2011, the Fields Institute, Toronto, Canada . Klavdija Kutnar, Quasi m-Cayley strongly regular graphs, "SOD02012 - Symmetries of Discrete Objects", February 13 - 17, 2012, Queenstown, New Zealand. Aleksander Malnič, On the split structure of lifted groups, I, "SOD02012 - Symmetries of Discrete Objects" February 13 - 17, 2012, Queenstown, New Zealand. Klavdija Kutnar, Cubic Cayleygraphs and snarks, International Conference on Cycles in Graphs, Nashville, USA, May 30 - June 2, 2012 (Invited Speaker). Dragan Marušič, Hamiltonicity of cubic Cayley graphs, International Conference on Cycles in Graphs, Nashville, USA, May 30 - June 2, 2012 (Invited Speaker). Istvan Kovacs, Characterization of cyclic Schur groups, AAA84 84th Workshop on General Algebra, Dresden, Germany, June 8 -10, 2012 Klavdija Kutnar, Distance-transitive graphs admit semiregular automorphisms, MDA 2012 - Mathematics of Distances and Applications, Varna, Bulgaria, July 2 - July 5, 2012 (Invited Speaker). Dragan Marušič, An infinite family of half-arc-transitive graphs with universal reachability relation, MDA 2012 -Mathematics of Distances and Applications, Varna, Bulgaria, July 2 - July 5, 2012 (Invited Speaker). Aleksander Malnič, On the split structure of lifted groups, I, MDA 2012 - Mathematics of Distances and Applications, Varna, Bulgaria, July 2 - July 5, 2012 (Invited Speaker). Martin Milanič, Equistable graphs: conjectures, results, and connections with Boolean functions, 25th European Conference on Operational Research, Vilnius (Lithuania), July 8-11, 2012. Martin Milanič, Uniqueness of independence polynomials in monogenic graph classes, International Colloquium on Graphs and Optimization 2012, Leukerbad, Switzerland, August 13-17, 2012. 7th Slovenian International Conference on Graph Theory 19-25 June 2011, Bled, Slovenia • Martin Skoviera: Snarks - Recent development (keynote lecture) • Jan Karabaš: Classification of Edge-transitive Maps Michal Kotrb"cik: High-genus Embeddings • Martin Ma"caj: Nonorientable Regular Maps Over Linear Fractional Groups • Roman Nedela: Asymptotic Enumeration of ReversibleMaps Regardless of Genus 23rd British Combinatorial Conference University of Exeter, 4-8 July, 2011. • Jozef Širan, Nonorientable regular maps of any given type over linear fractional groups IWONT 2011 International Workshop on Optimal Network Topologies Brussels, Belgium, July 11 -15, 2011 • Jana Siagiova: Cayley graphs in the degree-diameter problem (keynote lecture) • Martin Knor: On 3-arc graphs • Martin Macaj: Search for properties ofthe missing Moore graph • Maria Zdimalova: A family of large vertex-transitive graphs of diameter 2 Group Actions on Combinatorial Structures Beijing, August 21-27, 2011 • Martin Skoviera Regular maps with nilpotent automorphism groups • JanKarabaš: Discretegroupsof automorphismsoforientablesurfaces • Roman Nedela: Discrete groups of automorphisms of surfaces with given genus • Jozef Siran: External symmetries of regular maps Workshop on Symmetry in Graphs, Maps, and Polytopes Fields Institute Toronto, October 24-27, 2011 • Martin Skoviera: Regular maps with nilpotent automorphism groups • Jan Karabas: Classification ofedge-transitive maps • Martin Macaj: Nonorientable Regular Maps and Residual Finiteness ofTriangle Groups • Roman Nedela: Vertex Transitive and Edge Transitive Polytopes and 2-Dimensional Orbifolds • JozefSiran: External Symmetries of Regular and Orientably Regular Maps AMS Special Session on Topological Graph Theory, Structure and Symmetry, Boston, January 4-7, 2012 • Martin Skoviera: Locally Maximal Embeddings of Graphs in Orientable Surfaces (invited lecture) • Roman Nedela: A recent progress in map enumerations (invited lecture) • Roman Nedela: Vertex transitive polyhedral maps and actions of discrete groups on surfaces (invited lecture) ATCAGC 2012 Workshop on Algebraic, Topological and Complexity Aspects of Graph Covers 26th - 31st January 2012, Eugene, Oregon • Roman Nedela: Flows and graph coverings SODO 2012 Symmetries of Discrete Objects Conference and MAGMA Workshop Queenstown, New Zealand, 1217 February 2012 • Jan Karabas: Discrete group actions on orientable surfaces • Martin Macaj: On the Wilson operators • JozefSiran: Imprimitivityoflocallyfinite, 1-ended, planargraphs Eurogiga Midterm Conference Prague, July 9-13, 2012 • Martin Skoviera: Regular maps with nilpotent automorphism groups (invited lecture) IWONT 2012 The 5th International Workshop on Optimal Network Topologies July 27 - 29, 2012 Institut Teknologi Bandung, Indonesia • Jozef Siran: A survey of algebraic methods in the degree-diameter problem (keynote lecture) • Martin Knor: Graphs with given degree and diameter on the smallest number ofvertices • Jana Siagiova: Quotients of large vertex-transitive and Cayley graphs ofgiven degree and diameter ACCOTA 2012 International Workshop Combinatorial and Computational Aspects of Optimization, Topology and Algebra December 3 to 7, 2012. Huatulco, Oaxaca, Mexico • Martin Skoviera: Odd decompositions of regular eulerian graphs of odd orders • JozefSiran: Algebraic methods in the degree-diameter problem T. Pisanski, Abstract polygonal complexes (with an application to synthetic biology), GEMS 13, Smolenice, Slovakia, July 2013 (invited speaker) T. Pisanski, An interplay between topological graph theory and synthetic biology, Second Joint International Meeting ofthe Israel Mathematical Union and the American Mathematical Society, Tel Aviv, Israel, June 2014 S. Cabello, The clique problem in ray intersection graphs, Congress of the Spanish Mathematical Society, Santiago de Compostela, Spain, Januar 2013. S. Cabello, Computing the stretch of an embedded graph, XV Spanish Meeting on Computational Geometry, Sevilla, Spain, June 2013. S. Cabello, Stackelberg shortest path tree game, revisited, 12th International Symposium on Operational Research in Slovenia, Dolenjske Toplice, September 2013. S. Cabello, Parameterized complexity of 1-planarity, BIRS Workshop: Geometric and Topological Graph Theory, Banff, Canada, september 2013. S. Cabello, Parameterized complexity of 1-planarity, Dagstuhl seminar: Algorithms for Optimization Problems in Planar Graphs, Dagstuhl, Germany, October 2013. D. Marušič, Semiregular subgroups of transitive permutation groups, 22nd Workshop '3inl', Kroczyce, Poland, November 2013 (invited speaker). D. Marušič, On prime-valent symmetric bicirculants and Cayley snarks, 1st Interna- tional Conference "Geometric science of information", GSI 2013, Pariz, France, Avgust 2013. P. Potočnik, On covers ofdoubled cycles, 5th International Workshop on Algebraic, Topological and Complexity Aspects of Graph Covers, Bovec, Slovenia, January 2013. P. Potočnik, How many symmetries can a symmetric graph have?, 37th Australian Conference on Combinatorial Mathematics and Combinatorial Computing, Perth, Australia, December 2013. V. Batagelj, Big data: Networks from data bases, Undicesima conferenza nazionale di statistica, Rome, Italy, February 2013 (invited speaker) V. Batagelj, Analysis of Large Bibliographic Networks, 4th In- ternational Workshop on Social Network Analysis: Networks in Space and Time (ARS'13), Rome, Italy, June 2013 (invited speaker). V. Batagelj, Introduction to network analysis, Short Phd Course, The Economics of Innovative Change; Dept. of Economics of the Friedrich Schiller University and the Max Planck Institute of Economics, Jena, Germany, July 2013. V. Batagelj, Introduction in network analysis, dvotedenski te"caj na 8th ECPR (Eu- ropean Consortium for Political Research) Summer School in Methods and Techniques, Fakulteta za družbene vede, Ljubljana, Slovenia, July/August 2013. V. Batagelj, Analysis of citation networks, Daegu International Social Network Conference (DISC'13), Daegu, South Korea, December 2013 (invited speaker). V. Batagelj, Symbolic clustering of users and antennae, 3rd conference on the Analysis of Mobile Phone Datasets, NetMob, Cambridge (Massachusetts), USA, May 2013._ V. Batagelj, Visualization oftraffic, 3rd conference on the Analysis of Mobile Phone Datasets, NetMob, Cambridge (Massachusetts), USA, May 2013. V. Batagelj, Workshop: Analysis of large networks with Pajek, XXXIII International Sunbelt Social Network Conference, Hamburg, Germany, May 2013. V. Batagelj, Approaches to Analysis of Citation Networks, XXXIII International SunbeltSocial Network Conference, Hamburg, Nem"cija, maj 2013. V. Batagelj, Analysis of Bibliographic Networks on "Social Networks", XXXIII In- ternational Sunbelt Social Network Conference, Hamburg, Germany, May 2013. V. Batagelj, Pajek tutorial, 4th International Workshop on Social Network Analysis: Networks in Space and Time (ARS'13), Rome, Italy, June 2013. V. Batagelj, Analysis of Large Bibliographic Networks: Collaboration Networks, INSNA'13, Xi'an, China, July 2013. V. Batagelj, Clustering of US counties based on their demographic structures, Confe- rence ofthe International Federation ofClassification Societies, IFCS- 2013, Tilburg, Netherlands, July 2013. V. Batagelj, On collecting the sport networks data from the web, 5th conference of the European Survey Research Association, Ljubljana, Slovenia, July 2013. V. Batagelj, Analysis of bibliometric networks, 27th Leoben-Ljubljana Graph The- ory seminar, Graz, Austra, September 2013. A. Bauer, An effect system for algebraic effects and handlers, 5th Conference on Algebra and Coalgebra in ComputerScience, Warsaw, Poland, September2013 (invited lecture). A. Bauer, Geometric realization of r-Tamari lattices, CSASC 2013, Koper, Slovenia, June 2013. A. Bauer, Number of standard strong marked tableaux, 25th International Confe- rence on Formal Power Series and Algebraic Combinatorics (FPSAC 2013), Paris, France, June 2013. A. Bauer, Results and conjectures on the number of standard strong marked ta- bleaux, European Conference on Combinatorics, Graph Theory and Applications - Eurocomb 2013, Pisa, Italy, September 2013. T. Pisanski, TheCover, 5th International Workshop on Alge- braic, Topological and Complexity Aspects of Graph Covers, Bovec, January/February 2013 (invited lecture) T. Biyikoglu, "Discrete and continuous models in the theory of networks" Cooperation Group Meeting, Center for Interdisciplinary Research (ZiF), Bielefeld, Germany, May 2013 (invited speaker). 7th Slovenian International Conference on Graph Theory, Bled, Slovenia, June 19-25, 2011 • Peter F. Stadler: Orthology Relations and the Reconciliation of Gene and Species Trees. • Lydia Ostermeier: Square Property and Equitable Partitions. Eurogiga Midterm Conference, Prague, Czech Republic, July 9-13, 2012 • Lydia Ostermeier: Square Property and Equitable Partitions. Indo-Slovenia Conference on Graph Theory and Applications, Thiruvananthapuram, India, February 22-24, 2013 • Peter F. Stadler: Graph grammars and directed hypergraphs: Discrete models of chemistry. (Plenary talk) • Matjaž Kovše: Topological representations of partial cubes. (Invited talk) • Lydia Ostermeier: Grid Property and Product-like Hypergraphs. First International Conference in Code Biology, Paris, France, May, 20-24, 2014 Peter F. Stadler: Graph grammars and the Analysis of Large (Bio)chemical Networks. K.Hu: Classification and enumeration of cyclic regular coverings of the platonic maps, Algebraic, Topological and ComplexityAspects ofGraph Covers, Bovec, Slovenia, 28. l.-l. 2. 2013 (invited speaker). R. Nedela: Recent progress in map enumeration, Geometry Days in Novosibirsk, Novosibirsk- öt-tna univerzita, Novosibirsk, Russia, 23.-27. 8. 2013 (invited speaker). R. Nedela: Half-arc-transitive actions with cyclic stabilizers and their geometric visualisation, International Conference on Graph Theory and Combinatorics DM60, Koper, Slovenia, 1.-3. 5. 2013 (invited speaker). R. Nedela: Recent development in classification of regular embeddings of graphs, 2nd International Conference on Group Actions and Transitive Graphs, Kunming, China, 4.-9. 9. 2013 (invited speaker). J. Širan: How symmetric can maps on surfaces be? 24th British Combinatorial Conference BCC 2013, Royal Holloway, University of London, UK, 30. 6. - 5. 7. 2013 (invited speaker). J. Širan: Regular maps on a given surface, TGT25 - The 25th International Workshop in Topological Graph Theory, Yokohama National University, Japan, 18.-22. 11. 2013 (invited speaker). M. Škoviera: Cycle bases, matchings, and the maximim genus ofgraphs, Indo-Slovenia Conference on Graph Theory & Applications, Thiruvananthapuram, India, 22.-24. 2. 2013 (invited speaker). M. Škoviera: Hamilton cycles in truncated triangulations, TGT25 - The 25th International Workshop in Topological Graph Theory, Yokohama National University, Japan, 18.-22. 11. 2013 (invited speaker). B. Candrakova: The circular chromatic index of line graphs of cubic snarks, 7th Czech-Slovak International Symposium on Graph Theory, Combinatorics Algorithms and Applications, Koöice, 11.07.2013. B. Candrakova: The circular chromatic index of k-regular graphs, EuroComb 2013, Pisa, Taliansko, 9.-13. 9. 2013. K. Hu: Group extensions and coverings of maps, Graph Embeddings and Maps on Surfaces, GEMS 2013, Smolenice, 14.-19. 7. 2013. K. Hu: Almost totally branched coverings over the platonic maps, 2nd International Conference on Group Actions and Transitive Graphs, Kunming, China, 4.-9. 9. 2013. J. Karabas: Discrete group actions on orientable surfaces, Algebraic, Topological and Complexity Aspects ofGraph Covers, Bovec, Slovenia, 28. l.-l. 2. 2013. J. Karabas: Discrete Group Actions on Orientable Surfaces, Geometry Days in Novosibirsk, Novosibirsk- öt-tna univerzita, Novosibirsk, Russia, 23.-27. 8. 2013. M. Kotrbčik: Locally maximal embeddings, Geometric and Topological Graph Theory, Bristol, UK, 15.nl9. 4. 2013. M. Kotrbčik: Genus of amalgamations of complete and complete bipartite graphs, 7th Czech-Slovak International Symposium on Graph Theory, Combinatorics Algorithms and Applications, Koöice, 11.07.2013. M. Kotrbik: Locally maximal embeddings, Graph Embeddings and Maps on Surfaces, GEMS 2013, Smolenice, 14,19. 7. 2013. M. Kotrbčik: Locally maximal ofgraphs in orientable surfaces, EuroComb 2013, Pisa, Taliansko, 9.-13. 9. 2013. M. Knor: Fullerene-like maps on hyperbolic surfaces, Geometric and Topological Graph Theory, Bristol, UK, 15.nl9. 4. 2013. M. Knor: Efficient domination in cubic vertex-transitive graphs on $2лп$ vertices, PhD Summer School in Discrete Mathematics, Rogla, Slovenia, 16.-21. 6. 2013. M. Knor: Efficient domination in 3-valent vertex-transitive graphs, 7th Czech-Slovak International Symposium on Graph Theory, Combinatorics Algorithms and Applications, Koöice, 7.-13. 7. 2013. M. Knor: Graphical models of hyperbolic fullerenes, Graph Embeddings and Maps on Surfaces, Graph Embeddings and Maps on Surfaces, GEMS 2013, Smolenice, 14.-19. 7. 2013. M. Knor: Deterministic models of self-similar networks, Cycles and Colourings, Nov" Smokovec, 8.-13. 9. 2013. M. Knor: Deterministic models of self-similar complex networks, 3inl, Kroczyce, 28.-30. 11. 2013. R. Lukotka: Avoiding 7-circuits in 2-factors of cubic graphs, 7th Czech-Slovak International Symposium on Graph Theory, Combinatorics Algorithms and Applications, Koöice, 7.-13. 7. 2013. R. Lukotka: Degenerate induced subgraphs of planar graphs, EuroComb 2013, Pisa, Italy, 9.-13. 9. 2013. M. Mačaj: Vertex-transitive graphs of given degree and diameter, Joint Mathematical Conference CSASC 2013, Koper, Slovenia, 9.-13. 6. 2013. E. Mačajova: On even cycle decompositions of 4-regular line graphs, 7th Czech-Slovak International Symposium on Graph Theory, Combinatorics Algorithms and Applications, Koöice, 7.-13. 7. 2013. E. Mačajova: Snarks with large oddness and small number of vertices, Eurocomb 2013, Pisa, 9.-13. 9. 2013. J. Mazak: Circumference of cubic graphs, 7th Czech-Slovak International Symposium on Graph Theory, Combinatorics Algorithms and Applications, Koöice, 7.-13. 7. 2013. J. Mazak: Non-trivial snarks with given circular chromatic index, Eurocomb 2013, Pisa, 9.-13. 9. 2013. R. Nedela: Branched covers over Platonic maps, Joint Mathematical Conference CSASC 2013, Koper, Slovenia, 9,13. 6. 2013. R. Nedela: Archimedean operations on maps, 7th Czech-Slovak International Symposium on Graph Theory, Combinatorics Algorithms and Applications, Košice, 7.-13. 7. 2013. R. Nedela: Hamilton cycles in truncated triangulations, 3inl, Kroczyce, 28.-30. 11. 2013. E. Rollova: Nowhere-zero flows on products of graphs, 7th Workshop on the Matthews-Sumner Conjecture and Related Problems, Domaülice, Czech republic, 24.-29. 3. 2013. E. Rollova: Signed homomorphisms of planar signed graphs to signed projective cubes, 7th Czech-Slovak International Symposium on Graph Theory, Combinatorics, Algorithms and Applications, Košice, 7.-13. 7. 2013. E. Rollova: Signed homomorphisms of planar signed graphs to signed projective cubes, EuroComb 2013, Pisa, Italy, 9.-13. 9. 2013. J. Šiagova: Lifting constructions of large vertex-transitive and Cayley graphs ofgiven degree and diameter, 7th Czech-Slovak International Symposium on Graph Theory, Combinatorics, Algorithms and Applications, Košice, 7,13. 7. 2013. J. Širan: Large vertex-transitive graphs of diameter two and given degree from finite projective planes, 7th Czech-Slovak International Symposium on Graph Theory, Combinatorics, Algorithms and Applications, Košice, 7.-13. 7. 2013. M. Škoviera: Cycle bases, matchings, and the maximim genus ofgraphs, Geometric and Topological Graph Theory, Bristol, UK, 15.nl9. 4. 2013. R. Nedela, Graph coverings and harmonic functions of graphs, 2014 Joint Math. Meetings of AMS and MAA, AMS Special Session on Topological Graph Theory: Structure and Symmetry Baltimore, 15.-18. 1. 2014. (invited talk) M. Škoviera, Bounding the order of a regular map with nilpotent automorphism group, 2014 Joint Math. Meetings ofAMS and MAA, AMS Special Session on Topological Graph Theory: Structure and Symmetry Baltimore, 15.-18. 1. 2014. (invited talk) Snježana Majstorović, Euro Mini Conference XXVIII on Variable Neighborhood Search, 4-7.10.2012, Herceg Novi, Montenegro. "A Variable Neighborhood Search Algorithm for Multiobjective Optimization in Graph Theory" (joint work with Gilles Caporrossi) Snježana Majstorović, Midsummer Combinatorial Workshop XIX, srpanj 2013, Prague, "Spectrum of modularity matrix of graphs" Tanja Vojković, 11. EuroGIGA Final Conference, 17-21.1.2014, Berlin, "Agents and distributed keys" JelenaSedlar, 11. EuroGIGAFinalConference, 17-21.1.2014, Berlin, "Remoteness, proximityandfewother distance invariants in graphs" Damir Vukičević, 11. EuroGIGA Final Conference, 17-21.1.2014, Berlin, "Distributed keys and agents" Tanja Vojković, 12. CompleNet, Bologna, 12-14.3. 2014., "Agents and key distribution" (joint work with Damir Vukičević and Vinko Zlatić) S.Majstorović, 13. Adriatic Conference on Graph Theory and Complexity, Split, 25-27.4.2014., "Bounds and relations on the betweenness centrality of graphs" D.Vukičević , 13. Adriatic Conference on Graph Theory and Complexity, Split, 25-27.4.2014., "Protecting Secrets by Distributed Keys" T.Vojković, 13. Adriatic Conference on Graph Theory and Complexity, Split, 25-27.4.2014., "Agents and Missing Persons in Networks with Distributed Keys" A.KIobučar, Conference on Operation Reseach KOI 2014, Osijek, Croatia, September 24-26,2014, "Roman domination number on cardinal product of paths and cycles" KLAVŽAR, Sandi, Wiener index in weighted graphs. V: 15th Workshop on Graph Theory: Colourings, Independence and Domination, Szklarska Poraba 2013, September 15-20. KLAVŽAR, Sandi. Two applicable network families: Fibonacci cubes and Sierpinski graphs. V: 12th International Symposium on Operational Research in Slovenia Dolenjske Toplice, Slovenia, September 25-27, 2013 (invited talk). KLAVŽAR, Sandi. Two theorems on distances in graphs isometrically embeddable into Cartesian product graphs. V: EuroGIGA Final Conference, Freie Universität Berlin, February 17-21, 2014. KLAVŽAR, Sandi. Some new results and approaches on the Szeged index and the Wiener index ofgraphs. V: 10th Meeting ofthe International Academy of Mathematical Chemistry, Split, June 7-10, 2014. KLAVŽAR, Sandi. Recent developments on the cut method. V: 5th KIAS Combinatorics Workshop, Korea Institute for Advanced Study, Seoul, Korea, September 26 - 27, 2014. The 5th KIAS Combinatorial Workshop. Seoul: KIAS, 2014 (invited talk). Associate partners Berman, L. W. Fields Institute Thematic Program on Discrete Geometry and Applications: Workshop on Symmetry in Graphs, Maps and Polytopes, Oct 24 -- 27, 2011, http://www.fields.utoronto.ca/programs/scientific/ll-12/discretegeom/talks/october.html M. Conder. 'The smallest regular polytopes of each rank1. Presented at 35th Australasian Conference on Combinatorial Mathematics and Combinatorial Computing, Melbourne, Australia, December 2011 M. Conder. ~A new approach to finding covers of arc-transitive graphs'. Presented at Workshop on Algebraic, Topological and Complexity Aspects ofGraph Covers (ATCAGC 2012), Eugene, Oregon, USA, January 2012. M. Conder. 'Finitely-presented groups in MAGMA1. Presented at Conference on Symmetries ofDiscrete Objects (SODO 2012), Queenstown, New Zealand, February 2012. M. Conder. 'The orders of symmetric graphs'. Presented at SIAM Conference on Discrete Mathematics, Halifax, Nova Scotia, Canada, June 2012. M. Conder. 'The intersection condition for regular polytopes1. Presented at Workshop on Abstract Polytopes (WAP 2012), Cuernavaca, Mexico, July 2012. M. Conder. 'Graph Symmetries'. Presented at 36th Australasian Conference on Combinatorial Mathematics and Combinatorial Computing (36ACCMCC), Sydney, Australia, December 2012. P. W. Fowler. Ruđer Bošković Institute, Zagreb, 3 July 2012. Invited lecture in series: Eminentni znanstvenici na IRB (Distinguished Scientists at the RBI) Fries numbers of benzenoids - even faulty algorithms can be interesting (invited talk) P. W. Fowler. Croatian Academy ofSciences and Arts, Invited lecture 'Aromaticity and counting', November 2012. (invitedtalk) P. W. Fowler. Invited contributor to Fields Institute of Mathematics (Toronto) to meeting on mathematical asp Rigidity and Symmetry, Oct 2011 (invited talk) M. Klin, conference SSAOS 2012 (High Tatras) see https://sites.google.com/site/ssalgebra2012/program Title: New non-Schurian association schemes with a few clases (invited talk) W. Imrich. 13.-17. February, 2012. SODO 2012, Conference on "Symmetries of Discrete Objects". Queenstown, New Zealand Lecture "Distinguishing Infinite Graphs". W. Imrich. 12. March, 2012, Lecture in Maribor "Distinguishing Infinite Graphs". W. Imrich. 28.-31. March and 15.-19. April, 2012 (Blocked course, three weeks). AGH Cracow, "The direct product and large networks". W. Imrich. 4. May till 14. June, 2012 Graph Theory Semester, University of Primorska, Koper, Slovenia Lectures on "Symmetry Breaking in Graphs" W. Imrich. 24.-30. June, 1012. 3rd SYGN Workshop and 2012 PhD Summer School Discrete Mathematics Rogla, Slovenia W. Imrich. 1.-5. Juli 2012. 6th European Congress of Mathematics, Cracow. Lecture "The endomorphism distinguishing number ofgraphs". W. Imrich. 18. September, 2012. Lecture at Renyi Institute ofthe Academy ofSciences . in budapest on "Symmetry Breaking in Graphs". W. Imrich. 20. September, 2012. lOYears Bioinformatics Leipzig W. Imrich. 1.-3. October 2012. International Symposium on Complex Network Analysis UMIT, Hall in Tirol Lecture on "Networks and Products ofGraphs". W. Imrich. 19. 0ctober2012. Lecture in Klagenfurt "Netzwerke". W. Imrich. 12. November 2012. Lecture University of Maribor "Symmetry Breaking in Graphs". W. Imrich. 25. November until 7. December, 2012 (Two-week blocked course) in Cracow on "Symmetry breaking in graphs". (More detailed than in Koper.) W. Imrich. 21st Workshop '3inl' 2012, Cracow, Poland. 29. November -1. December 2012. Lecture "On the infinite Motion conjecture for Graphs and Groups". D. Leemans: Symmetries of Discrete Objects 2012, Queenstown (NewZealand), Febru- ary 13-17, 2012. Magma Minicourse on Permutation Groups, 2 lectures. D. Leemans: New Zealand Mathematical Society Colloquium, Auckland (New Zealand), December 6-8, 2011. Polytopes of high rank for the symmetric groups. D. Leemans: Workshop on Symmetry, Graphs and Polytopes, Fields Institute, Toronto (Canada), October 24-27, 2011. Plenary talk. Polytopes of high rank arising from almost simple groups. D. Leemans: Seventh Slovenian International Conference on Graph Theory, Bled (Slovenia), June 20-25, 2011. Chirally regular polytopes. D. Leemans: 5th De Bru 'n Workshop on Groups, Combinatorics and Computing, NUI Galway (Ireland), April 1116, 2011. Searching for Geometries with Magma. Leydold, Josef. 2011. Convex Cycle Bases and Cartesian Products. 25th LL-Seminar on Graph Theory, Leoben, Österreich, 23.09.-24.09. Leydold, Josef. 2012. Generating Generalized Inverse Gaussian Distributed Random Variates. Monte Carlo and Quasi-Monte Carlo Methods 2012, Sydney, Australien, 13.02.-17.02. Leydold, Josef. 2011. Convex Cycle Bases. 7th Slovenian International Conference on Graph Theory, Bled, Slowenien, 20.06.-24.06. Lecture at IWONT 2014 Bratislava June 30-July4, Patrick Fowler (The University ofSheffield), Why chemists care about graph theory? Invited Plenary Speaker at MAGIC (Workshop on Magnetically Induced Currents in Chemistry, University of Helsinki, Tvarminne, Finland, Nov 17-21 2014), Patrick Fowler: The orbital view: selection rules for ring-current aromaticity. M. Conder. 'More on symmetric regular covers of graphs'. Presented at Workshop on Algebraic, Topological and Complexity Aspects of Graph Covers (ATCAGC 2013), Bovec, Slovenia. January 2013. M. Conder. 'Some unexpected consequences of computation with groups'. Presented at Retirement Symposium forTomTucker, Colgate University, Hamilton NY. April 2013. M. Conder. 'Discrete objects with maximum possible symmetry'. Presented at American Mathematical Society meeting, Boston, MA. 6 April - 7 April 2013. M. Conder. 'Half-arc-transitive and semi-symmetric graphs'. Presented at International Conference on Graph Theory & Combinatorics, Koper, Slovenia. May 2013. M. Conder. 'Graph Symmetries'. Presented at PhD summer school on Discrete Mathematics, Rogla, Slovenia. June 2013. M. Conder. 'An update on polytopes with many symmetries'. Presented at Retrospective Workshop on Discrete Geometry, Optimization & Symmetry, Fields Institute, Toronto. November 2013. M. Conder. 'Embeddings of circulants on surfaces'. Presented at 37th Australasian Conference on Combinatorial Mathematics & Combinatorial Computing (37ACCMCC), Perth, Australia. December 2013. M. Conder. 'Embeddings ofcirculants on surfaces'. Presented at Annual Meeting ofthe American Math Society, Baltimore MD, USA. January 2014. M. Conder. 'Regular maps with simple underlying graph1. Presented at Algebraic, Topological and Complexity Aspects of Graph Covers, Ostravice, Czech Republic. January 2014. M. Conder. 'Extreme graph symmetries'. Presented at Algebraic Combinatorics: Spectral Graph Theory, Erdös-Ko-Rado Theorems and Quantum Information Theory, Waterloo, Canada. June 2014. M. Conder. 'Skew morphisms ofgroups'. Presented at Symmetries of Graphs and Networks IV, Rogla, Slovenia. June 2014. M. Conder. 'Recent developments in the study of regular maps'. Presented at Symmetries In Graph, Maps And Polytopes (SIGMAP'14) - plenary lecture, West Malvern, UK. July 2014. M. Conder. 'Minimum genus embeddings ofvertex-transitive graphs'. Presented at Embedded Graphs, Euler Mathematical Institute, St Petersburg, Russia. October 2014. - Posters Computers in Scientific Discovery conference, August 2012, Portorož (Slovenia) // Ivona Puljic: Upper and lower bound for Roman domination number of cardinal product of paths, (which was a joint work with Croatian PI Antoaneta Klobučar) CSASC Conference, Koper, Slovenia, Juny 2013. Antoaneta Klobučar "Some results for Roman domination number on cardinal products of paths and cycles" (joint work with Ivona Puljić) M. Cerinšek, J. Bodlaj, V. Batagelj, Symbolic clustering of users and antennae, 3rd Conference on the Analysis of Mobile Phone Datasets, NetMob 2013, Cambridge (Massachusetts), USA, May 2013, Mobile phone data for development: analysis of mobile phone datasets for the development of Ivory Coast, 211-226. J. Bodlaj, M. Cerinšek, V. Batagelj, Visualization of traffic, 3rd Conference on the Analysis of Mobile Phone Datasets, NetMob 2013, Cambridge (Massachusetts), USA, May 2013, Mobile phone data for development: analysis of mobile phone datasets for the development of Ivory Coast, 480-495. - Other (please define) Balakrishnan, R. and Bapat, R. B. and Klavžzar, Sandi and, Preface [Recent trends in graph theory and combinatorics].Discrete Math. 312 (2012), 1493. http://dx.doi.Org/10.1016/j.disc.2011.12.025 (Introduction) Bratislava Graph Theory Seminar (Regular seminar on graph theory and combinatorics) Head of the seminar: Martin Skoviera Weekly (during the semester) at Comenius University, Bratislava Slovakia SeminarforDiscreteMatematics, Institute ofMathematics, Physicsand Mechanics, Ljubljana. Headofthe seminar: Tomaž Pisanski. Annual meeting ofthe Slovak part ofthe GReGAS team. December 5 to 12 2011 and December 11 to 15 2012 Mosonmagyarovar, Hungary AGT in BB Algebraic Graph Theory in Banska Bystrica, August/September 2012, Matej Bel University, Banska Bystrica Slovakia • Programme Committee: Mikhail Klin, Roman Nedela and Martin Macaj (all members of GReGAS) • Organizing Committee: Martin Macaj, Jan Karabas (both GReGAS) and Stefan Gyurki In addition, Slovenian PL and PI teams achieved the following: • Organization ofthe conference Computers in Scientific Discovery with a plenary speaker, prof. Harold Kroto, nobel laureate (discovery ofC60 fulleren) • proj. member prof. Konvalinka received award of University of Ljubljana given to best teachers. • A project financed by Picker Institute (USA, Colgate University) continued into the 2nd year as the results for the first year were very good. • Pisanski appointed to the Publications Committee of European Mathematical Society. • PI prof. Marusic was elected as rector ofthe University of Primorska. • project member prof. Miklavic received national award for science (Zois prize). • V. Batagelj has received INSNA's William D. Richards Jr., Software Award (2013) for Pajek software Unpublished lecture: Leydold, Josef. 2012. Sign patterns ofgraph laplacian eigenvectors. Istanbul Discrete Mathematics Meetings, Istanbul, 27.04. Bratislava Graph Theory seminar (lead by Prof. M. Škoviera), http://new.dcs.fmph.uniba.sk/index.php/Seminare/SeminarZTeorieGrafov Regular seminar in Banska Bystrica: "Aka si mi krasna" (lead by doc. M. Haviar), http://www.akasimikrasna.sk R. Nedela: Why mathematicians compute maps? MIST conference, Кжак, 7.-12. 1. 2013. J. Širan: Fruits of ploughing fields along elliptic curves, MIST conference, Klak, 7.-12. 1. 2013. Public outreach - Press releases / - National / international newspaper articles (presenting your CRP or part of your work) Article related to the conference and EUROGIGA networking event and especially about nobelist Sir Harald Kroto visiting Slovenia having talk at CSD 6 conference. • http://www.dnevnik.si/magazin/znanost-in-tehnologija/1042548265 • http://www.primorska.info/novice/18840/nobelovec_kroto_predaval_na_turistici • http://www.slomedia.it/dr-kroto-znanost-je-predvsem-nacin-razmisljanja - TV appearance Croatian Academy ofSciences and Arts, Invited lecture 'Aromaticity and counting', November 2012. (invited talk) Short interview about this second lecture was recorded for Croatian TV - Radio appearance / - Other (please define) / Other activities / outputs - Patents_ / - Websites http://www.gregas.eu - Official project web site http://atlas.gregas.eu - Encyclopediaofgraphswebsite - Other (please define) • Abelium team: o in 2012 won Slovenian innovation award for the most innovative service iOliva (geometric graph theory application) o in 2013 won Slovenian innovation award for the most innovative business model (use of graph theory and optimization in logistics for cooperation in GoOpti solution: Abelium team and TMVista company) o In 2014, finalist of the Cloud Innovation World Cup (one of the four finalists for Allianz Evolve Award, Abelium & TM Vista) o In 2014 winner of Eurocloud Europe Award for the cloud solution with the best business impact (Goopti solution, Abelium & TMVista) B.5. Feedback on the EUROCORES programme and EUROCORES scheme (up to 300 words) / Section C. Self-assessment and follow-up C.l. Overall self assessment on the accomplishments of the CRP (up to 600 words) Initially not all PI members of the project were approved by their respective countries, among them J. Leydold from Austria and D. Leemans from Belgium. Professor Leydold then continued to work as a member ofthe PI Stadler, while D. Leemans moved to New Zealand and continued cooperation through the team of AP Conder. Thus, even without all the Pis from the initial application, the work on the project started successfully. After that the project was carried out according to the plan in the application without any major deviations. For a brief period there was unclear situation in regard to financing of PI Biyikoglu, which was eventually resolved. Funding was temporarly stopped or reduced due to government budget cuts addressing the economic crisis in Croatia and Slovenia. Financing issues made the work on the project harder but did not have a major impact on the course ofthe project. Beside the topics stated in the application the course ofthe research has even extended, especially in the part of applications in chemistry, bioinformatics and large networks. The reporting related to the project was carried out on national levels according to the reporting obligations of the respective national research agencies. We have successfully submitted the midterm report to ESF and received a positive feedback. The CRP contributed significantly in strenghthening research and cooperation ties, which were built in the past through series of periodic conferences and workshops, existing personal collaboration and common scientific journal Ars Mathematica Contemporanea. After the start of indexing by SCIE in 2011, the journal grew stronger and in 2015 we plan to double the number of issues per year (4 instead of 2). The work in CRP contributed significantly towards this achievement. The teams of Slovenian Pis involved cooperation of all three major universities in Slovenia and also a research oriented company Abelium, which is kind of a spin-off from the two universities (University of Ljubljana, University of Primorska). Thus the research and development received the motivation from industry especially related to applications of large networks in logistics. The project offered a strong funding support for the groups involved, which could in this way continue and expand their scientific work. During this period all groups have supported several young scientists, some of them very progressive ones. C.2. Follow-up activities emerged as a result of the CRP and the programme (up to 300 words) New applications ofgraph representations in chemistry and synthetic biology were identified. An application to the ERASynBiol call was sent and a project BioOrigami was approved, starting in 2015, includes PI Pisanski. PI Pisanski and PI Klavžar become involved in research in applications ofgraph and representation theory in synthetic biology. Several papers were published already. The journal established by the groups involved in the CRP, Ars Mathematica Contemporanea, grew stronger and in 2015 we plan to double the number of issues per year from 2 to 4. The work on evolution in networks opened new research directions, especially considering the motivation from the "Big-data" industry. New initiative related to formalization and software development, similar to the one of Pajek from the 90s, have started in 2014. As a result ofthis, two new prototype software libraries, TQ and lanus were developed and the ideas presented on relevant international conferences. We have started to work on graph modelling of multi party off-the-record communication with Berkant Ustaoglu (Izmir Institute ofTechnology). Based on the results ofthe CRP, proposal forthe prestigiousTUBITAK 1003 - Primary Subjects R&D Funding Program was submitted and is currently pending in the second round. De novo Peptide Sequencing is an important problem in computational mass spectrometry based proteomics. In cooperation with Jens Allmer Bioinformatics group Izmir Institute ofTechnology we have efficiently solved de novo sequencing problem with a new novel linear time algorithm as a result of this CRP. Jens Allmer has a start-up company funded by TUBITAK. Our results have shown a huge economical potential and also potential for future research funding. Bilateral project Slovenia-Croatia has been established, with the leaders Damir Vukičević and Dragan Stevanović. "Adriatic Conference on Graph Theory and Complexity" was held for the first time (in Split, Croatia, April 2014.). C.3. Forward looking perspectives enabled by the programme (up to 300 words) During the time of the duration of the CRP, the general R&D focus in EU have changed significantly and positively - problems from the real-world, industry and business are becoming increasingly important motivator for R&D. Conseqently, the research is becoming more and more multidisciplinary. This move is clearly seen in the orientation ofthe Horizon 2020 calls and work programmes. We are glad that this has reflected within our CRP as well, since our research became increasingly more motivated toward R&D and applications in synthetic biology, chemistry, bioinformatics, Big-data, data science and logistics. This expansion from basic research towards interdisciplinary collaboration and applications, while still keeping strong "basic" component, opens up opportunities for involving mathematicians in Horizon 2020 projects and similar. For mathematicians it is often difficult to involve into EU projects like the ones of FP6 and FP7. The kind of projects like EUROGiga are important initiatives, which together with multidisciplinarity pressure from the Horizon's 2020 side, opens up the space for involving mathematicians into R&D possibly having much bigger socio-economic impact. So we strongly support future initiatives similar to EUROCORES/EUROGiga. Priloga 3 VEDA / Področje / Podpodročje: 1.07.01/Naravoslovno-matematične vede/Računalniško intenzivne metode in aplikacije/Algoritmi Dosežek: GÖMEZ-NÜNEZ, Antonio J., BATAGELJ, Vladimir, VARGAS-QUESADA, Benjamin, MOYA-ANEGÖN, Felix de, CHINCHILLA-RODRIGUEZ, Zaida. Optimizing SCImago Journal & Country Rank classification by community detection. Journal of informetrics, ISSN 1751-1577, 2014, vol. 8, iss. 2, str. 369-383. http://dx.doi.org/10.1016/Moi.2014.01.011. [COBISS.SI-ID 17105241] kategorija: 1A1 (Z, A'', A', A1/2); uvrstitev: SSCI, Scopus (d), Scopus, MBP; tipologijo je verificiral OSICD Vir: http://dx.doi.org/10.1016/uoi.2014.01.011 Povzetek: Klasifikacija predstavlja pomebno temo v bibliometriji in scientometriji. Želimo si zanesljivih in doslednih orodij ter rezultatov. Takšni cilji zahtevajo dobro opredeljen sistem razvrščanja po osnovnem predmetu, ki ustrezno odraža znanstvena področja. V širšem naboru tehnik razvrščanja so metode za razvrščanje (ang. cluster analysis) ene izmed najbolj uspešnih metod. Dva algoritma za razvrščanje, ki temeljita na modularnosti - metodi VOS in Louvain - sta predstavljeni z namenom posodobitve in optimizacije razvrstitev na platformi SCImago Journal & Country Rank (SJR). Uporabili smo orodje za analizo in vizualizacijo omrežij Pajek in zagnali oba algoritma na omrežju z več kot 18.000 revij v SJR, ki združuje tri mere za neposredno citiranje, sosklic in sklicno sklopljenost. Množica tako pridobljenih skupin je bila poimenovana po kategorijah oznak, dodeljenih revijam v SJR in po pomembnih besedah iz naslovov revij. Kljub temu, da rezultata obeh algoritmov odražata majhne razlike, rezultati kažejo podobno obnašanje pri združevanju revij. Zato predstavljata ustrezni rešitvi za namene razvrščanja. Na novo ustvarjeni klasifikaciji temelječi na dveh algoritmih smo primerjali z drugimi bibliografskimi sistemi razvrščanja, vključno z originalnimi predmetnimi kategorijami v SJR in WoS, da bi preverili njihovo skladnost, ustreznost in natančnost. Poleg nekaterih pomembnih razlik, smo identificirali določeno povezanost in homogenost med štirimi analiziranimi sistemi za klasifikacijo.